Question

A vertical pole casts a shadow along the level ground. What is the angle of elevation of the sun from the ground when the length of the shadow is 5555% of the height of the pole? Give your answer in degrees and round to 2 decimal places.

Answer 1

To find the angle of elevation of the sun when the length of the shadow is 5555% of the height of the pole, we can use similar triangles and the definition of tangent. The angle of elevation is approximately 60.97 degrees.

Step-by-step explanation:

To find the angle of elevation of the sun, we can use the concept of similar triangles.

Let's assume the height of the pole is h and the length of the shadow is s.

According to the given information, the length of the shadow is 5555% of the height of the pole, which can be written as 5555% = 55.55% = 0.5555. So, s = 0.5555h.

Using the definition of tangent, we can write:

tan(angle of elevation) = opposite/adjacent = h/s

Substituting the value of s, we get:

tan(angle of elevation) = h/(0.5555h) = 1/0.5555

Using a calculator, we can find that the angle of elevation is approximately 60.97 degrees. Rounded to 2 decimal places, the angle of elevation of the sun from the ground is 60.97 degrees.