Question

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

Answer 1

Answer:

14 ft  

Step-by-step 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,



$l = \sqrt{196.06}$


$l = 14.00$