Question

Suppose you stand 53 ft from a wind farm turbine. Your angle of elevation to the hub of the turbine is 56.5^{\circ} ∘ . Your eye level is 5.5 ft above the ground. To the nearest tenth, how tall is the turbine from the ground to its hub?

Answer 1

Let's denote the height of the turbine from the ground to its hub as "h". We can use trigonometry to solve for "h".

First, we need to find the distance from the observer's eye level to the base of the turbine. We can use the angle of elevation and the observer's distance from the turbine to find this distance.

Using the tangent function:

tan(56.5°) = h / (53 ft + 5.5 ft)

Simplifying and solving for "h":

h = tan(56.5°) * (53 ft + 5.5 ft)

h = 67.8 ft

Therefore, the height of the turbine from the ground to its hub is approximately 67.8 ft to the nearest tenth.