Question

A tree house is being constructed with support beams that create right triangles. If the legs of the triangle created measure 2.5 ft. and 3 ft., what are the angle measures of the non-right angles?
(1 point)
Responses

39.8° and 50.2°
39.8° and 50.2°

68.5° and 21.5°
68.5° and 21.5°

87.6° and 2.4°
87.6° and 2.4°

56.4° and 33.6°

Answer 1

To find the measures of the non-right angles of a right triangle, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side.

Given:
- One leg (opposite) = 2.5 ft
- Other leg (adjacent) = 3 ft

We can find one of the non-right angles, say \( \theta \), using the tangent function:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2.5}{3}
\]

Now we calculate \( \theta \):
\[
\theta = \tan^{-1}\left(\frac{2.5}{3}\right)
\]
Calculating this gives:
\[
\theta \approx \tan^{-1}(0.8333) \approx 39.8°
\]

Now, since the triangle is a right triangle (90°), we can find the other non-right angle by subtracting \( \theta \) from 90°:
\[
90° - 39.8° = 50.2°
\]

So, the angle measures of the non-right angles are approximately:
\[
39.8° \text{ and } 50.2°
\]

Therefore, the correct response is:
**39.8° and 50.2°**.