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 hundredths place
Answers
GPT-4o mini
To find the height of the flagpole, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation to the opposite side (the height of the flagpole) and the adjacent side (the length of the shadow).
The formula for the tangent of an angle in a right triangle is given by:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Let \( h \) be the height of the flagpole. In this scenario:
- \(\theta = 25\) degrees
- The length of the shadow (adjacent side) = 137 feet
Using the tangent function:
\[
\tan(25^\circ) = \frac{h}{137}
\]
To solve for \( h \), we rearrange the equation:
\[
h = 137 \cdot \tan(25^\circ)
\]
Now we can calculate \( \tan(25^\circ) \) using a calculator:
\[
\tan(25^\circ) \approx 0.4663
\]
Now plug this value into the equation:
\[
h \approx 137 \cdot 0.4663 \approx 64.0161
\]
Rounding to the hundredths place:
\[
h \approx 64.02
\]
Therefore, the height of the flagpole is approximately **64.02 feet**.
The formula for the tangent of an angle in a right triangle is given by:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Let \( h \) be the height of the flagpole. In this scenario:
- \(\theta = 25\) degrees
- The length of the shadow (adjacent side) = 137 feet
Using the tangent function:
\[
\tan(25^\circ) = \frac{h}{137}
\]
To solve for \( h \), we rearrange the equation:
\[
h = 137 \cdot \tan(25^\circ)
\]
Now we can calculate \( \tan(25^\circ) \) using a calculator:
\[
\tan(25^\circ) \approx 0.4663
\]
Now plug this value into the equation:
\[
h \approx 137 \cdot 0.4663 \approx 64.0161
\]
Rounding to the hundredths place:
\[
h \approx 64.02
\]
Therefore, the height of the flagpole is approximately **64.02 feet**.