Question

Find the indicated missing angle. Round your answer to the nearest tenth.
the sides are 13 12 5 also has a right angle


(5 points)
Responses

67.4 degrees
67.4 degrees

22.6 degrees
22.6 degrees

21.0 degrees

Answer 1

To find the missing angle in the triangle with sides of lengths 13, 12, and 5 (where one angle is a right angle), we can apply the sine, cosine, or tangent functions. Let's denote the sides as follows:

- Side a = 5 (the shortest side)
- Side b = 12
- Side c = 13 (the hypotenuse)

Since one angle is a right angle, we can use the trigonometric functions based on the right triangle relationships.

We can find the angle opposite to side a (5) using the sine function.

\[
\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{13}
\]

Now we can find angle A:

\[
A = \arcsin\left(\frac{5}{13}\right)
\]

Calculating this gives:

\[
A \approx \arcsin(0.3846) \approx 22.6^\circ \quad (\text{rounded to the nearest tenth})
\]

Thus, the missing angle is approximately **22.6 degrees**.

So the correct response is **22.6 degrees**.