Question

To calculate the cost of painting his silo, a farmer must find its height. The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below. Approximate the height of the silo, rounded to the nearest foot.

Answer 1

Answer:

Height of the silo = 18 feet.

Step-by-step explanation:

From the figure attached BC is the length of the silo and the height of the farmer is 5 ft.

Farmer is standing at 8 ft distance from the silo.

From triangle AEC,

tan(∠CAE) = $\frac{CE}{AE}$

                 = $\frac{5}{8}$

m(∠CAE) = $tan^{-1}(\frac{5}{8})$

               = 32°

m∠BAE = 90° - 32° = 58°

From the triangle ABE,

tan58° = $\frac{BE}{AE}$

BE = 8tan58°

BE = 12.8 ft

Total height of the silo = BE + EC

                                         = 12.8 + 5

                                         = 17.8

                                         ≈ 18 ft          

Therefore, total height of the silo is 18 ft.