Question

A flagpole casts a shadow that is 137 feet long. The angle of elevation from the end of the shadow to the top of the flagpole is 25 degrees. How tall is the flagpole? rounding to the hundreths

Answer 1

To find the height of the flagpole, we can use trigonometry. In this case, we can apply the tangent function, which relates the angle of elevation, the height of the flagpole, and the length of the shadow.

The tangent of the angle of elevation is defined as the opposite side (the height of the flagpole) over the adjacent side (the length of the shadow).

Let \( h \) be the height of the flagpole. The equation can be set up as:

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

Substituting the known values:

\[
\tan(25^\circ) = \frac{h}{137}
\]

Now, solve for \( h \):

\[
h = 137 \cdot \tan(25^\circ)
\]

Using a calculator to find \( \tan(25^\circ) \):

\[
\tan(25^\circ) \approx 0.4663
\]

Now substituting this value back into the equation:

\[
h \approx 137 \cdot 0.4663 \approx 64.0651
\]

Rounding to the hundredths place, the height of the flagpole is:

\[
\boxed{64.07} \text{ feet}
\]