Question

A 4.9-m wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 25 degrees above the horizon. How deep is the pool?

Answer 1

Step-by-step explanation:

We can solve this problem using trigonometry. Let's draw a diagram:

|\

| \

| \ <- Sun rays

| \

| \

| \

| \

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Pool

The angle between the sun rays and the horizontal line is 90 - 25 = 65 degrees. Let's call the depth of the pool "d". We want to find the value of "d" that makes the bottom of the pool completely shaded.

We can see that the triangle formed by the sun rays, the top edge of the pool, and the bottom edge of the shaded area is a right triangle. The angle between the sun rays and the top edge of the pool is also 65 degrees, because the top edge is parallel to the ground.

Using trigonometry, we can write:

tan(65 degrees) = d / 4.9 m

Solving for "d", we get:

d = 4.9 m * tan(65 degrees)

Using a calculator, we find:

d ≈ 13.7 m

Therefore, the pool is approximately 13.7 meters deep.