Question

Use the inverse of cosine to find the missing angle. Round your answer to the nearest tenth. (1 point) θ≈ °

θ is between sides, one is 12 and the other is 9

Answer 1

To find the missing angle \( \theta \) between the sides of lengths 12 and 9, you can use the cosine rule. The cosine rule states that for any triangle, the cosine of an angle can be found using the lengths of the sides.

However, if you have the lengths of two sides and you want to find the angle between them, you can directly apply the cosine formula:

\[
\cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab}
\]

Where:
- \( a \) and \( b \) are the lengths of the two sides (in this case, 12 and 9),
- \( c \) is the length of the side opposite the angle \( \theta \).

If we do not know \( c \), we cannot find \( \theta \) specifically. However, if you meant to find the angle whose adjacent side is 12 and opposite side is 9, you could use:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12}
\]

Thus,

\[
\theta = \tan^{-1}\left(\frac{9}{12}\right)
\]

Calculating \( \theta \):

1. First calculate \( \frac{9}{12} = 0.75 \).
2. Now take the arctangent:
\[
\theta = \tan^{-1}(0.75)
\]
Using a calculator, you find:

\[
\theta \approx 36.87^\circ
\]

Rounding to the nearest tenth, the angle \( \theta \) is approximately:

\[
\theta \approx 36.9^\circ
\]

So the answer is:

\[
\theta \approx 36.9^\circ
\]