Question

The cross section of a hopper for containing balls is shown.

What is the length of the top of the hopper?



Enter your answer in the box.

Round only your final answer to the nearest foot.

Answer 1

14 ft

Explanation:

If we label the vertices ABC as in the diagram below, we can use the law of cosines to calculate the third side AB of the triangle.

Data:

a = 13

b = 15

C = 59.5°

Calculation:

c² = a² + b² -2abcosC

= 13² + 15² - 2 × 13 × 15cos59.5

= 169 + 225 - 390 × 0.5075

= 394 - 197.9

= 196.1

c = √ 196.1

= 14 ft

Answer 2

ANSWER


`14 \: ft`



EXPLANATION

Let the top of the hopper be


`l \: ft`


Then, by the cosine rule,


`{l}^(2) = {13}^(2) + {15}^(2) - 2(15)(13) \cos(59.5 \degree)`

We evaluate to get,


`{l}^(2) = 169 + 225 - 390\cos(59.5 \degree)`



`{l}^(2) = 394 - 197.94`




`{l}^(2) = 196.06`
Take positive square root of both sides to get,




`l = √(196.06)`



`l = 14.00`