Question

How do I calculate the angle θ in a right triangle where the height of the flagpole is 30 feet and the distance from the person to the flagpole is 20 feet?

Answer 1

To calculate the angle \( \theta \) in a right triangle formed by the height of the flagpole and the distance from the person to the flagpole, you can use the tangent function. In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

Here, the height of the flagpole (opposite side) is 30 feet, and the distance from the person to the flagpole (adjacent side) is 20 feet. This relationship can be expressed with the formula:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{30}{20}
\]

Now, simplifying the fraction:

\[
\tan(\theta) = \frac{30}{20} = \frac{3}{2}
\]

To find \( \theta \), you need to take the arctangent (inverse tangent) of \( \frac{3}{2} \):

\[
\theta = \tan^{-1}\left(\frac{3}{2}\right)
\]

Using a calculator or trigonometric tables, compute the value:

\[
\theta \approx 56.31^\circ
\]

Therefore, the angle \( \theta \) is approximately \( 56.31^\circ \).