Question

Use the inverse of the tangent ratio to find the approximate measure of the missing angle. Round your answer to the nearest whole degree.
Imagine a right triangle. The line on the side of it is labelled "2 cm" and the bottom line is labelled "5 cm". Inside the triangle the bottom right point has the sin label.

Answer 1

To find the missing angle in a right triangle using the inverse of the tangent ratio, we need to identify which sides correspond to the tangent function. In a right triangle, the tangent of an angle is given by the ratio of the length of the opposite side to the length of the adjacent side.

In your description, you mentioned:
- The opposite side (to the angle we are trying to find) is labeled "2 cm."
- The adjacent side is labeled "5 cm."

The tangent of the angle \( \theta \) can be expressed as:

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

To find the angle \( \theta \), you can take the inverse tangent (arctan) of the ratio:

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

Now, using a calculator, let's calculate this value:

\[
\theta \approx \tan^{-1}(0.4) \approx 21.8^\circ
\]

Rounding this to the nearest whole degree, we get:

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

Therefore, the approximate measure of the missing angle is **22 degrees**.