Question

The hypotenuse of a right triangle is 5 inches. If one leg is 2 inches, find the degree measure of each angle.

Short answer

So, the angles of right triangle are$23.6°,66.4°,90°.$

Step-by-step solution

Given Information

Given that the hypotenuse of a right triangle is 5 inches and one leg is 2 inches.

Solution

We can draw a figure of the given problem as: -

So in $△ABC$

$$\begin{gathered} \sin \left(x\right)=\frac{AB}{AC} \\ \sin \left(x\right)=\frac{2}{5} \\ x={\sin }^{-1}\left(\frac{2}{5}\right) \\ x\approx 23.6° \end{gathered}$$

So, angle C is $23.6°$.

Now angle A is $180°-(\angle B+\angle C).$

$$\begin{gathered} \angle A=180°-(90°+23.6°) \\ \angle A=66.4° \end{gathered}$$