Question
use the inverse of cosine to find the missing angle 12, 9. Round your answer to the nearest tenth
Answers
GPT-4o mini
To find the missing angle using the inverse cosine function, you can use the following formula which involves the cosine of the angle:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
In your case, if you have adjacent side = 9 and hypotenuse = 12, then:
\[
\cos(\theta) = \frac{9}{12} = \frac{3}{4}
\]
Now, to find the angle \(\theta\), you will take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{3}{4}\right)
\]
Using a calculator to find \(\theta\):
\[
\theta \approx \cos^{-1}(0.75) \approx 41.4^\circ
\]
Therefore, rounded to the nearest tenth, the missing angle is approximately **41.4 degrees**.
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
In your case, if you have adjacent side = 9 and hypotenuse = 12, then:
\[
\cos(\theta) = \frac{9}{12} = \frac{3}{4}
\]
Now, to find the angle \(\theta\), you will take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{3}{4}\right)
\]
Using a calculator to find \(\theta\):
\[
\theta \approx \cos^{-1}(0.75) \approx 41.4^\circ
\]
Therefore, rounded to the nearest tenth, the missing angle is approximately **41.4 degrees**.