The sun is 25º above the horizon.Find the length of a shadow cast by a building that is $\alpha = 130$ feet tall (see figure).Approximate the answer to two decimal places.? ?
A)281.79 ft
B)278.79 ft
C)279.79 ft
D)280.79 ft
E)282.79 ft

Question

The sun is 25º above the horizon.Find the length of a shadow cast by a building that is $\alpha = 130$ feet tall (see figure).Approximate the answer to two decimal places.?  ?
A)281.79 ft 
B)278.79 ft 
C)279.79 ft 
D)280.79 ft 
E)282.79 ft

Quizplus · Accepted Answer

Using basic trigonometry, we can set up the following equation:
tan(25º) = height of the building / length of the shadow
tan(25º) = 11 / length of the shadow
length of the shadow = 11 / tan(25º) ≈ 278.79 ft
Therefore, the best choice is B, which is the closest approximation to the calculated length of the shadow.

The Sun Is 25º Above the Horizon α=130\alpha = 130α=130 Feet Tall (See Figure)

The Sun Is 25º Above the Horizon $\alpha = 130$ Feet Tall (See Figure)