Question

Use the image to answer the question.

The sides and angles of a right triangle are labeled.

Use the inverse of cosine to find the approximate measure of the missing angle the triangla sides are 56 33 65
.

(1 point)
Responses

59.5°
59.5°

30.5°
30.5°

43°
43°

90°

Answer 1

In a right triangle, the sum of the angles is 180°, and one of the angles is already 90°. To find the missing angle, we will use the cosine rule and the inverse cosine function.

Let’s identify the sides:
- The longest side (hypotenuse) is 65.
- The other two sides are 56 and 33.

We'll assume we're looking for the angle opposite to the side of length 33. We will use the formula:

\[
\cos(A) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]

In this case, the adjacent side to angle A is 56, and the hypotenuse is 65.

Now, let's calculate:

\[
\cos(A) = \frac{56}{65}
\]

Next, we calculate the value of \(\cos(A)\):

\[
\cos(A) \approx 0.8615
\]

Now, we find the angle A using the inverse cosine:

\[
A = \cos^{-1}(0.8615)
\]

Calculating that:

\[
A \approx 30.5°
\]

Thus, the approximate measure of the missing angle is:

**30.5°**