Question

J) The angle of elevation from Mindy to a cell phone tower is 75 degrees. If Mindy is standing 28
feet from the base of the tower, find the height of the cell phone tower. Round your answer to the
nearest tenth. (one decimal place) (1 point)
height of the cell phone tower =

Answer 1

To find the height of the cell phone tower, you can use the tangent of the angle of elevation. The relationship can be expressed with the formula:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case:
- \(\theta = 75\) degrees (the angle of elevation),
- The opposite side is the height of the cell phone tower (let's call it \(h\)),
- The adjacent side is the distance from Mindy to the base of the tower, which is 28 feet.

So, we can set up the equation:

\[
\tan(75^\circ) = \frac{h}{28}
\]

Now, solve for \(h\):

\[
h = 28 \cdot \tan(75^\circ)
\]

Next, we calculate \(\tan(75^\circ)\):

\[
\tan(75^\circ) \approx 3.732
\]

Now we can substitute this value back into the equation:

\[
h \approx 28 \cdot 3.732 \approx 104.496
\]

Rounding to the nearest tenth, the height of the cell phone tower is:

\[
\text{Height of the cell phone tower} \approx 104.5 \text{ feet}
\]

So, the final answer is:

\[
\text{height of the cell phone tower} \approx 104.5
\]