Question

There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36°. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38°. Find the height of the lightning rod.The lightning rod is Answer feet tall.

Answer 1

The height of the lightning rod = 27.37 ft

Step-by-step explanation

The given parameters can be represented as shown in the figure below:

What to find:

The height of the lightning rod, h₁.

Step-by-step solution:

The height of the lightning rod, h₁ can be calculated using h₁ = H - h₂

Using trigonometric function

`tan\text{ }\theta=(opposite)/(Adjacent)`

To find h₂,

`\begin{gathered} tan\text{ }36^0=(h_2)/(500) \\ h_2=tan\text{ }36^0*500 \\ h_2=0.7265*500 \\ h_2=363.27\text{ }ft \end{gathered}`

To find H,

`\begin{gathered} tan\text{ }38=(H)/(500) \\ Cross\text{ multiply} \\ H=tan\text{ }38*500 \\ H=0.7812*500 \\ H=390.64\text{ }ft \end{gathered}`

Since h₂ = 363.27 ft, and H = 390.64 ft, then

h₁ = 390.64 ft - 363.27 ft = 27.37 ft