Question

A 64-inch tall person casts a 50-inch shadow. At what angle do the sun's rays hit the ground? Round your answer to the nearest tenth.

a. 37.9 degrees
b. 46.6 degrees
c. 53.1 degrees
d. 60.2 degrees

Answer 1

Using the tangent function, the angle at which the sun's rays hit the ground is approximately 52.1 degrees. We calculate this by taking the arctan of the person's height to shadow length ratio (64 inches to 50 inches). None of the options perfectly match, but the closest is 53.1 degrees.

Step-by-step explanation:

The question is asking for the angle at which the sun's rays hit the ground, given that a 64-inch person is casting a 50-inch shadow. To find the angle, we can use the tangent function (tan) from trigonometry.

We can set up the following equation:

tan(angle) = opposite/adjacent = person's height/shadow length

tan(angle) = 64/50

Now, we need to find the angle whose tangent is 64/50. Using a calculator, we find the angle by taking:

angle = arctan(64/50)

angle ≈ 52.125 degrees

Therefore, the angle rounded to the nearest tenth is 52.1 degrees. So, none of the provided options (a) 37.9 degrees, (b) 46.6 degrees, (c) 53.1 degrees, or (d) 60.2 degrees fully match our calculated angle. However, the closest answer among the options would be (c) 53.1 degrees.