Question

Find the measure of ∠A
. Round your answer to the nearest whole degree.
sides are 8 17 15 also has a right angle


(5 points)
Responses

28 degrees
28 degrees

62 degrees
62 degrees

41 degrees
41 degrees

Answer 1

Given the triangle with sides of lengths 8, 17, and 15, and knowing that one of the angles is a right angle, we can use the Pythagorean theorem to find the measures of the angles.

Assuming that the triangle is a right triangle with the longest side (17) being the hypotenuse, let’s check:

1. Check if it's a right triangle:

\[
8^2 + 15^2 = 64 + 225 = 289
\]
\[
17^2 = 289
\]

Since \(8^2 + 15^2 = 17^2\), we confirm that this is indeed a right triangle.

2. We know that if \( \angle A \) is opposite to the side of length 8, to find it we can use the sine function because we have a right triangle. We can find \( \angle A \) using:

\[
\sin(\angle A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{17}
\]

3. Now we can find \( \angle A \):

Using the inverse sine function:

\[
\angle A = \sin^{-1}\left(\frac{8}{17}\right)
\]

Calculating this value using a calculator:

\[
\angle A \approx 28.4 \text{ degrees}
\]

4. Rounding to the nearest whole degree, \( \angle A \approx 28 \text{ degrees} \).

Thus, the correct response is:

**28 degrees**.