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. (1 point) θ≈ °
between 2cm and 5cm is the 90 degree angle, θ is in the angle on the other end of the 5cm

Answer 1

To find the angle \(\theta\) using the inverse of the tangent function, we can set up the relationship based on the tangent ratio, which is defined as:

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

In your case, the opposite side is 2 cm (the length opposite to angle \(\theta\)), and the adjacent side is 5 cm (the length next to angle \(\theta\)). Therefore, we can express it as:

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

To find \(\theta\), we take the inverse tangent (arctan) of both sides:

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

Now we can calculate it:

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

Using a calculator:

\[
\theta \approx 21.8^\circ
\]

Rounding to the nearest whole degree, we find:

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

So, the approximate measure of the missing angle \(\theta\) is:

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