A monument stands on level ground. The angle of elevation of the top of the monument, taken at a
point 425 feet from the foot of the monument, is 32º. Find the height of the monument to the nearest
foot.
To find the height of the monument, we can use the tangent of the angle of elevation. The tangent of an angle is the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the monument, and the adjacent side is the distance from the foot of the monument to the point where the angle of elevation is measured.
We can use the formula:
tan(angle) = opposite/adjacent
Let's plug in the values we know:
tan(32°) = opposite/425
Now we can solve for the height (opposite side) of the monument:
opposite = tan(32°) * 425
Using a calculator, we get:
opposite ≈ 0.6249 * 425
opposite ≈ 265.55625
So, the height of the monument is approximately 265.55625 feet. Rounded to the nearest foot, the height of the monument is 266 feet.