Question

Someone please help me with this

Answer 1

50° is the correct answer

Explanation:

Right Triangles

The right triangles are identified because they have an internal angle of 90°. The basic trigonometric ratios can be used to find angles and side lengths as needed.

We have a right triangle with the following characteristics:

The hypotenuse is 13 units long

The indicated angle is opposite to the leg of 10 units long.

When we know the length of the opposite side, we use the sine ratio. Let's call θ to the required angle:

`\displaystyle \sin\theta=\frac{\text{opposite side}}{\text{hypotenuse}}`

`\displaystyle \sin\theta=(10)/(13)`

Using a calculator set in mode degrees, the angle is:

`\theta=\sin^(-1)(10)/(13)`

`\theta\approx 50.3^\circ`

First choice: 52° is not correct because is not a good approximation to 50.3°

Second choice:38° is not correct because is not a good approximation to 50.3°

Third choice: 50° is a good approximation to 50.3°. Correct Answer

Fourth choice: 40° is not correct because is not a good approximation to 50.3°