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

1. First, we need to identify the sides of the right triangle in this problem. The bottom of the flag forms the adjacent side, the height at which the diagonal ends forms the opposite side, and the diagonal itself is the hypotenuse.

2. The length of the adjacent side is the length of the flag, which is 20 meters. The length of the opposite side is the height at which the diagonal ends, which is 7 meters.

3. We can now use the tangent function to find the angle of elevation. The formula for the tangent of an angle (which we'll call θ) is:

tan(θ) = opposite / adjacent

4. Substituting the given lengths into this formula gives us:

tan(θ) = 7 / 20

5. To find the angle θ, we need to use the inverse tangent function, also known as the arctangent function. This function gives the angle whose tangent is a given number. So, we have:

θ = arctan(7 / 20)

6. Using a calculator to compute this gives us an angle of approximately 19.29 degrees.

7. Rounding this to the nearest tenth gives us 19.3 degrees.

So, the angle of elevation of the diagonal is approximately 19.3 degrees.

Question

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

1. First, we need to identify the sides of the right triangle in this problem. The bottom of the flag forms the adjacent side, the height at which the diagonal ends forms the opposite side, and the diagonal itself is the hypotenuse.

2. The length of the adjacent side is the length of the flag, which is 20 meters. The length of the opposite side is the height at which the diagonal ends, which is 7 meters.

3. We can now use the tangent function to find the angle of elevation. The formula for the tangent of an angle (which we'll call θ) is:

tan(θ) = opposite / adjacent

4. Substituting the given lengths into this formula gives us:

tan(θ) = 7 / 20

5. To find the angle θ, we need to use the inverse tangent function, also known as the arctangent function. This function gives the angle whose tangent is a given number. So, we have:

θ = arctan(7 / 20)

6. Using a calculator to compute this gives us an angle of approximately 19.29 degrees.

7. Rounding this to the nearest tenth gives us 19.3 degrees.

So, the angle of elevation of the diagonal is approximately 19.3 degrees.

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