Question

A right triangle is shown. The diagonal line measures a length of nine and the horizontal line measures 13. Use the inverse of the tangent ratio to find the indicated missing angle. Round your answer to the nearest whole degree. (1 point) θ≈ °

Answer 1

To find the missing angle \( \theta \) in a right triangle where the opposite side (vertical side) measures 9 and the adjacent side (horizontal side) measures 13, you can use the inverse tangent (also known as arctangent) function.

The tangent of an angle in a right triangle is given by the ratio of the opposite side to the adjacent side:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{13}
\]

To find the angle \( \theta \), you can use the inverse tangent:

\[
\theta = \tan^{-1}\left(\frac{9}{13}\right)
\]

Now, let's calculate that:

\[
\theta \approx \tan^{-1}(0.6923)
\]

Using a calculator, we find:

\[
\theta \approx 39.7^\circ
\]

Rounding this to the nearest whole degree gives:

\[
\theta \approx 40^\circ
\]

Therefore, the missing angle \( \theta \) is approximately **40 degrees**.