A 100 ft. long swimming pool is to be constructed. The pool will be 4 ft. deep at one end and 8 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end?

To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

1. First, we need to determine the length of the side opposite to the angle we're trying to find. This is the difference in depth between the deep end and the shallow end of the pool,

To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

1. First, we need to determine the length of the side opposite to the angle we're trying to find. This is the difference in depth between the deep end and the shallow end of the pool, which is 8 ft - 4 ft = 4 ft.

2. The length of the adjacent side is the length of the pool, which is 100 ft.

3. Now we can find the tangent of the angle, which is (opposite side) / (adjacent side) = 4 ft / 100 ft = 0.04.

4. To find the angle itself, we take the inverse tangent (also known as the arctangent) of this value. In most calculators, this function is denoted as "tan^-1".

5. So, the measure of the angle is tan^-1(0.04).

6. If you calculate it, you'll find that the angle is approximately 2.29 degrees.

So, to the nearest degree, the measure of the acute angle the bottom of the pool makes with the wall at the deep end is 2 degrees.

To solve this problem, we can use trigonometry. Specifically, we'll use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

1. First, we need to determine the length of the opposite side. This would be the difference in depth between the deep end and the shallow end of the pool, which is 8 ft - 4 ft = 4 ft.

2. The length of the adjacent side is the length of the pool, which is 100 ft.

3. Now we can find the tangent of the angle. The tangent of the angle (let's call it θ) is the opposite side divided by the adjacent side, or tan(θ) = 4 ft / 100 ft = 0.04.

4. To find the angle θ, we take the inverse tangent (also known as the arctangent) of 0.04. Using a calculator, arctan(0.04) ≈ 2.29 degrees.

So, to the nearest degree, the measure of the acute angle the bottom of the pool makes with the wall at the deep end is 2 degrees.