A man standing on level ground is 1000 feet away from the base of a 350-foot-tall building. Find,
to the nearest degree, the measure of the angle of elevation to the top of the building from the
point on the ground where the man is standing.
If you sketch the man and the building on paper, you'll have a right triangle. The right angle is the point where the wall of the building meets the ground. The height of the building is one leg of the triangle, the line on the ground from the building to the man's feet is the other leg, and the line from his feet to the top of the building is the hypotenuse.
We need to find the angle at his feet, between the hypotenuse and the leg of the triangle.
Well, the side opposite the angle is the height of the building -- 350ft, and the side adjacent to the angle is the distance from him to the building -- 1,000 ft.
The tangent of the angle is (opposite) / (adjacent)
= (350 ft) / (1,000 ft) = 0.350 .
To find the angle, use a book, a slide rule, a Curta, or a calculator to find the angle whose tangent is 0.350 .
