A person standing 34 meters from the foot of a chimney finds that the measure of the angle of elevation to the top of the chimney is 52 degrees. To the nearest tenth of a meter, find the height of the chimney.

h/34=sin52

solve for h

27 To find the height of the chimney, we can use trigonometry and set up a right triangle. The adjacent side of the triangle is the distance from the person to the foot of the chimney, which is 34 meters. The angle of elevation is the angle between the horizontal ground and the line of sight to the top of the chimney, which is 52 degrees.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the chimney (which we want to find), and we know the length of the adjacent side (34 meters).

So, we can use the tangent function to find the height:

tan(angle) = opposite/adjacent
tan(52 degrees) = height/34

To solve for the height, we can multiply both sides of the equation by 34:

height = 34 * tan(52 degrees)

Using a calculator, we can find:

height ≈ 34 * 1.2799 ≈ 43.5 meters.

Therefore, the height of the chimney is approximately 43.5 meters.