A person is standing 21 feet from a building. The angle of elevation between the person and the ground is 59°. Find the height of the building. (Round to the nearest hundredth)
assuming you meant that the angle of elevation between the person and the top of the building is 59°, the height h is
h/21 = tan59°
plug and chug to solve for h
35
To find the height of the building, we can use trigonometry. Specifically, we can use the tangent function.
Let's first draw a diagram to represent the situation. Label the height of the building as "h" and the distance from the person to the building as "d". We are given that the angle of elevation between the person and the ground is 59°.
Now, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building (h) and the adjacent side is the distance from the person to the building (d). Therefore, we have:
tan(59°) = h / d
Now, substitute the values we know into this equation. We are given that the person is standing 21 feet from the building, so d = 21. We want to solve for h, so rearrange the equation:
h = d * tan(59°)
Now, plug in the values and calculate:
h = 21 * tan(59°)
Using a scientific calculator or trigonometric tables, we find that tan(59°) is approximately 1.6643.
Now, calculate:
h ≈ 21 * 1.6643
h ≈ 34.94
Therefore, the height of the building is approximately 34.94 feet.