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?

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?

39.8 and 50.2 *****
68.5 and 21.5
87.6 and 2.4
56.4 and 33.6

Answer 1

1.A

2.A
3.A
unit 2 lesson 8 quick check

Answer 2

Correct : ) Using the tangent ratio.

Answer 3

To find the angle measures of the non-right angles in a right triangle, we can use trigonometric functions. Specifically, we can use the tangent function.

The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, the opposite side is 2.5 ft and the adjacent side is 3 ft.

Let's calculate the tangent of the angle:

tan(angle) = opposite/adjacent
tan(angle) = 2.5/3
tan(angle) ≈ 0.83333

Now, we need to find the angle whose tangent is approximately 0.83333. We can use the inverse tangent function (also known as arctan or tan^(-1)) to find this angle.

angle = arctan(0.83333)
angle ≈ 40.2788

So, one of the non-right angles is approximately 40.2788 degrees.

To find the other non-right angle, we can subtract the angle we just found from 90 degrees (since the sum of angles in a triangle is 180 degrees).

other angle = 90 - 40.2788
other angle ≈ 49.7212

Therefore, the angle measures of the non-right angles are approximately 40.2788 degrees and 49.7212 degrees.

Answer 4

To find the angle measures of the non-right angles in the triangle, you can use trigonometric ratios. In this case, we'll use the tangent ratio.

Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. The non-right angles are usually labeled as angle A and angle B, with the right angle being angle C.

Given that the legs of the triangle are 2.5 ft and 3 ft, the opposite side to angle A would be 2.5 ft, and the adjacent side would be 3 ft.

Now, let's find the tangent of angle A:
tan(A) = opposite/adjacent = 2.5/3

Using a calculator, we can find the value of tangent inverse (tan⁻¹) of this ratio.

tan⁻¹(2.5/3) ≈ 39.8°

So, angle A measures approximately 39.8°.

Since the sum of angles in a triangle is 180°, we can calculate angle B by subtracting the right angle and angle A from 180°.

Thus, angle B ≈ 180° - 90° - 39.8° ≈ 50.2°.

Therefore, the correct answer is 39.8° and 50.2°.