Question

if the sun is 57 degrees above the horizon, find the length of the shadow cast by a building 54 ft tall. Give your answer as a decimal rounded to the nearest tenth.

Answer 1

Explanation:

Using the ground as the base of a triangle and the building as the height,

the shadow cast would be the hypotenuse of a right triangle.

Sun is casting a 57 degree angle with the base and the hypotenuse, this question can be solved using sin ratio.

54 ft is the side opposite the 57° angle.

Let the hypotenuse or shadow = x

sin57° = 54/x

.8389 = 54/x

multiply each side by x

.8389x = 54/x · x

.8389x = 54

Divide each side by .8389

x = 64.37

round to 64.4 feet