Vectors

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The vector $\langle 2, 1 \rangle$ starts at the point $(1, 1)$ . Tap the point where it ends.
$P = (3, 3)$ and $Q = (8, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 11, 11 \rangle$
$P = (2, 2)$ and $Q = (8, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 10, 8 \rangle$
$P = (2, 2)$ and $Q = (8, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 3 \rangle$
2. $\langle -6, -3 \rangle$
3. $\langle 10, 7 \rangle$
$P = (1, 4)$ and $Q = (7, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 3 \rangle$
2. $\langle -6, -3 \rangle$
3. $\langle 8, 11 \rangle$
$P = (3, 4)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 9, 12 \rangle$
$P = (4, 1)$ and $Q = (5, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 5 \rangle$
2. $\langle -1, -5 \rangle$
3. $\langle 9, 7 \rangle$
$P = (4, 2)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 11, 8 \rangle$
$P = (4, 1)$ and $Q = (5, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 6 \rangle$
2. $\langle -1, -6 \rangle$
3. $\langle 9, 8 \rangle$
$P = (3, 3)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 9, 10 \rangle$
$P = (2, 3)$ and $Q = (6, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 6 \rangle$
2. $\langle -4, -6 \rangle$
3. $\langle 8, 12 \rangle$
$P = (1, 1)$ and $Q = (6, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 7, 7 \rangle$
$P = (2, 3)$ and $Q = (5, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 5 \rangle$
2. $\langle -3, -5 \rangle$
3. $\langle 7, 11 \rangle$
$P = (1, 2)$ and $Q = (8, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 7 \rangle$
2. $\langle -7, -7 \rangle$
3. $\langle 9, 11 \rangle$
$P = (3, 3)$ and $Q = (6, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 2 \rangle$
2. $\langle -3, -2 \rangle$
3. $\langle 9, 8 \rangle$
$P = (2, 4)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 2 \rangle$
2. $\langle -7, -2 \rangle$
3. $\langle 11, 10 \rangle$
$P = (4, 1)$ and $Q = (7, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 4 \rangle$
2. $\langle -3, -4 \rangle$
3. $\langle 11, 6 \rangle$
$P = (2, 2)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 6 \rangle$
2. $\langle -4, -6 \rangle$
3. $\langle 8, 10 \rangle$
$P = (2, 3)$ and $Q = (9, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 5 \rangle$
2. $\langle -7, -5 \rangle$
3. $\langle 11, 11 \rangle$
$P = (3, 4)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 9, 11 \rangle$
$P = (1, 1)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 8, 5 \rangle$
2. $\langle -8, -5 \rangle$
3. $\langle 10, 7 \rangle$
$P = (4, 3)$ and $Q = (7, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 6 \rangle$
2. $\langle -3, -6 \rangle$
3. $\langle 11, 12 \rangle$
$P = (3, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 12, 10 \rangle$
$P = (3, 1)$ and $Q = (9, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 8 \rangle$
2. $\langle -6, -8 \rangle$
3. $\langle 12, 10 \rangle$
$P = (4, 1)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 13, 7 \rangle$
$P = (2, 3)$ and $Q = (6, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 5 \rangle$
2. $\langle -4, -5 \rangle$
3. $\langle 8, 11 \rangle$
$P = (3, 1)$ and $Q = (8, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 8 \rangle$
2. $\langle -5, -8 \rangle$
3. $\langle 11, 10 \rangle$
$P = (1, 2)$ and $Q = (9, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 8, 3 \rangle$
2. $\langle -8, -3 \rangle$
3. $\langle 10, 7 \rangle$
$P = (4, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 4 \rangle$
2. $\langle -5, -4 \rangle$
3. $\langle 13, 10 \rangle$
$P = (3, 3)$ and $Q = (9, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 5 \rangle$
2. $\langle -6, -5 \rangle$
3. $\langle 12, 11 \rangle$
$P = (2, 2)$ and $Q = (9, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 7 \rangle$
2. $\langle -7, -7 \rangle$
3. $\langle 11, 11 \rangle$
$P = (2, 1)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 9, 7 \rangle$
$P = (1, 2)$ and $Q = (8, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 6 \rangle$
2. $\langle -7, -6 \rangle$
3. $\langle 9, 10 \rangle$
$P = (3, 1)$ and $Q = (7, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 7 \rangle$
2. $\langle -4, -7 \rangle$
3. $\langle 10, 9 \rangle$
$P = (1, 3)$ and $Q = (7, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 6 \rangle$
2. $\langle -6, -6 \rangle$
3. $\langle 8, 12 \rangle$
$P = (2, 2)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 7, 7 \rangle$
$P = (3, 3)$ and $Q = (6, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 3 \rangle$
2. $\langle -3, -3 \rangle$
3. $\langle 9, 9 \rangle$
$P = (2, 1)$ and $Q = (7, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 6 \rangle$
2. $\langle -5, -6 \rangle$
3. $\langle 9, 8 \rangle$
$P = (1, 1)$ and $Q = (6, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 6 \rangle$
2. $\langle -5, -6 \rangle$
3. $\langle 7, 8 \rangle$
$P = (2, 3)$ and $Q = (8, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 10, 10 \rangle$
$P = (4, 3)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 1, 2 \rangle$
2. $\langle -1, -2 \rangle$
3. $\langle 9, 8 \rangle$
$P = (2, 3)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 4 \rangle$
2. $\langle -7, -4 \rangle$
3. $\langle 11, 10 \rangle$
$P = (1, 1)$ and $Q = (8, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 4 \rangle$
2. $\langle -7, -4 \rangle$
3. $\langle 9, 6 \rangle$
$P = (1, 4)$ and $Q = (6, 9)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 7, 13 \rangle$
$P = (3, 1)$ and $Q = (8, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 5 \rangle$
2. $\langle -5, -5 \rangle$
3. $\langle 11, 7 \rangle$
$P = (3, 4)$ and $Q = (7, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 4, 2 \rangle$
2. $\langle -4, -2 \rangle$
3. $\langle 10, 10 \rangle$
$P = (3, 2)$ and $Q = (5, 5)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 2, 3 \rangle$
2. $\langle -2, -3 \rangle$
3. $\langle 8, 7 \rangle$
$P = (2, 4)$ and $Q = (7, 8)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 5, 4 \rangle$
2. $\langle -5, -4 \rangle$
3. $\langle 9, 12 \rangle$
$P = (2, 2)$ and $Q = (5, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 3, 5 \rangle$
2. $\langle -3, -5 \rangle$
3. $\langle 7, 9 \rangle$
$P = (2, 1)$ and $Q = (9, 7)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 7, 6 \rangle$
2. $\langle -7, -6 \rangle$
3. $\langle 11, 8 \rangle$
$P = (3, 2)$ and $Q = (9, 6)$ . Which vector is $\overrightarrow{PQ}$ ?
1. $\langle 6, 4 \rangle$
2. $\langle -6, -4 \rangle$
3. $\langle 12, 8 \rangle$
Find the exact magnitude of $\vec{v} = \langle 6, -5 \rangle$ .
Find the direction angle of $\langle 2, 3 \rangle$ , in degrees, to 1 decimal place.
Find the direction angle of $\langle -2, 3 \rangle$ , between $0^\circ$ and $360^\circ$ , to 1 decimal place.
$\vec{u} = \langle 4, 1 \rangle$ and $\vec{v} = \langle 5, 6 \rangle$ . Find the exact value of $|\vec{u} + \vec{v}|$ .
$\vec{u} = \langle 2, 3 \rangle$ and $\vec{v} = \langle -3, 1 \rangle$ , both starting at the origin. Tap the end point of $\vec{u} + \vec{v}$ .
Find the horizontal component of the unit vector in the direction of $\langle 3, 4 \rangle$ .
A ball is kicked at 51 meters per second, at $35^\circ$ above the ground. Find the horizontal component of its velocity, in meters per second, to 1 decimal place.Not to scale
Find $\langle 5, 2 \rangle \cdot \langle 8, -9 \rangle$ .
Are $\langle 6, 4 \rangle$ and $\langle -8, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 1 \rangle$ and $\langle -2, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 1 \rangle$ and $\langle -3, 18 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 4 \rangle$ and $\langle -8, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 6 \rangle$ and $\langle -12, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 6 \rangle$ and $\langle -12, 8 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 6 \rangle$ and $\langle -12, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 3 \rangle$ and $\langle -9, 9 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 4 \rangle$ and $\langle -8, 10 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 5 \rangle$ and $\langle -10, 10 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 1 \rangle$ and $\langle -2, 2 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 5 \rangle$ and $\langle -10, 8 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 4 \rangle$ and $\langle -8, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 4 \rangle$ and $\langle -12, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 2 \rangle$ and $\langle -6, 3 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 5 \rangle$ and $\langle -15, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 4 \rangle$ and $\langle -8, 8 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 6 \rangle$ and $\langle -18, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 4 \rangle$ and $\langle -12, 3 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 4 \rangle$ and $\langle -12, 9 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 5 \rangle$ and $\langle -10, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 1 \rangle$ and $\langle -2, 10 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 2 \rangle$ and $\langle -4, 10 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 1 \rangle$ and $\langle -3, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 3 \rangle$ and $\langle -6, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 5 \rangle$ and $\langle -15, 18 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 6 \rangle$ and $\langle -18, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 4, 3 \rangle$ and $\langle -9, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 3 \rangle$ and $\langle -6, 10 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 1 \rangle$ and $\langle -3, 9 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 3 \rangle$ and $\langle -6, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 1 \rangle$ and $\langle -3, 3 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 6 \rangle$ and $\langle -12, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 3 \rangle$ and $\langle -6, 2 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 4 \rangle$ and $\langle -8, 2 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 2 \rangle$ and $\langle -4, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 3 \rangle$ and $\langle -9, 15 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 6 \rangle$ and $\langle -18, 15 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 1 \rangle$ and $\langle -2, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 2 \rangle$ and $\langle -4, 4 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 2 \rangle$ and $\langle -6, 9 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 1 \rangle$ and $\langle -2, 12 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 2 \rangle$ and $\langle -6, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 2 \rangle$ and $\langle -4, 2 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 6, 6 \rangle$ and $\langle -18, 18 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 5 \rangle$ and $\langle -15, 15 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 5, 2 \rangle$ and $\langle -6, 15 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 3, 5 \rangle$ and $\langle -15, 9 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 1, 5 \rangle$ and $\langle -10, 2 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Are $\langle 2, 3 \rangle$ and $\langle -9, 6 \rangle$ perpendicular?
1. Yes: their dot product is 0
2. No: neither of them is the zero vector
3. No: their components do not add up to 0
Find the angle between $\langle 4, 4 \rangle$ and $\langle 4, -3 \rangle$ , in degrees, to 1 decimal place.
A plane flies due east at 101 miles per hour through the air, and the wind blows due north at 32 miles per hour. Find its speed over the ground, to 1 decimal place.Not to scale
Two people pull a box: one with 36 newtons due east, the other with 59 newtons due north. At what angle north of east does the box start to move? Give degrees to 1 decimal place.Not to scale

Answers

$(3, 2)$
$\langle 5, 5 \rangle$
$\sqrt{61}$
$\frac{180 \tan^{-1}{\left(\frac{3}{2} \right)}}{\pi}$
$- \frac{180 \tan^{-1}{\left(\frac{3}{2} \right)}}{\pi} + 180$
$\sqrt{130}$
$(-1, 4)$
$\frac{3}{5}$
$51 \cos{\left(\frac{7 \pi}{36} \right)}$
$22$
Yes: their dot product is 0
$\frac{180 \cos^{-1}{\left(\frac{\sqrt{2}}{10} \right)}}{\pi}$
$5 \sqrt{449}$
$\frac{180 \tan^{-1}{\left(\frac{59}{36} \right)}}{\pi}$