Question

Find the measure of θ . Round your answer to the nearest whole number. No hypotenuse, Adjacent = 5cm, Opposite = 2 cm

Answer 1

To find the angle \(\theta\) in a right triangle where you know the lengths of the opposite side and the adjacent side, you can use the tangent function:

\[
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
\]

In this case, the opposite side is 2 cm and the adjacent side is 5 cm:

\[
\tan(\theta) = \frac{2}{5}
\]

Next, you will use the arctangent function (also known as the inverse tangent) to find \(\theta\):

\[
\theta = \tan^{-1}\left(\frac{2}{5}\right)
\]

Using a calculator:

\[
\theta \approx 21.80^\circ
\]

Rounding to the nearest whole number:

\[
\theta \approx 22^\circ
\]

Therefore, the measure of \(\theta\) is approximately \(22^\circ\).