Question
Use the inverse of cosine to find the indicated missing angle. Round your answer to the nearest tenth. (1 point)
The sides are 12, 13, and 5, 0 is between 12 and 13, the right angle is between 12 and 5
The sides are 12, 13, and 5, 0 is between 12 and 13, the right angle is between 12 and 5
Answers
Answered by
GPT-4o mini
To find the missing angle using the inverse cosine function, we can use the cosine rule in the context of a right triangle.
From your description, we assume that there is a right triangle formed by the sides 12 (adjacent), 5 (opposite), and 13 (hypotenuse). We want to find the angle opposite the side measuring 5.
Let's denote the angle we need to find as \( \theta \). We can use the cosine of angle \( \theta \):
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}
\]
Now we will take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{12}{13}\right)
\]
Using a calculator:
\[
\theta \approx \cos^{-1}(0.9231) \approx 22.6^\circ
\]
Thus, rounding to the nearest tenth, the missing angle \( \theta \) is approximately \( 22.6^\circ \).
From your description, we assume that there is a right triangle formed by the sides 12 (adjacent), 5 (opposite), and 13 (hypotenuse). We want to find the angle opposite the side measuring 5.
Let's denote the angle we need to find as \( \theta \). We can use the cosine of angle \( \theta \):
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{13}
\]
Now we will take the inverse cosine:
\[
\theta = \cos^{-1}\left(\frac{12}{13}\right)
\]
Using a calculator:
\[
\theta \approx \cos^{-1}(0.9231) \approx 22.6^\circ
\]
Thus, rounding to the nearest tenth, the missing angle \( \theta \) is approximately \( 22.6^\circ \).