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

Height of the silo = 18 feet.

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) = CE/AE=5/8

m(∠CAE) = tan-1 (5/8)

= 32°

m∠BAE = 90° - 32° = 58°

From the triangle ABE,

tan58° = BE/AE

BE = 8tan58°

BE = 12.8 ft

Total height of the silo = BE + EC

= 12.8 + 5

= 17.8

≈ 18 ft

Therefore, the total height of the silo is 18 ft.

Answer 2

The silo's total height is 18 feet.

According to the attached diagram, BC is the length of the silo and the farmer's height is 5 feet.

The farmer is 8 feet away from the silo.

Triangle AEC,

tan(CAE) = CE/AE=5/8

m(CAE) = tan-1 (5/8)

= 32°

m∠BAE = 90° - 32° = 58°

From the triangle ABE,

tan58° = BE/AE

BE = 8tan58°

BE = 12.8 ft

Total silo height = BE + EC

= 12.8 + 5

= 17.8

≈ 18 ft

As a result, the silo's total height is 18 feet.