Question

Geometry

The hypotenuse of a right triangle is 12 feet. If one leg is 8 feet, find the degree measure of each angle.

Short answer

The angles of a triangle are

$$\begin{gathered} A=48.2 \\ B=41.8 \\ C=90 \end{gathered}$$

Step-by-step solution

Step 1. Given information

The given data is$$\begin{gathered} hypotenuse\left(h\right)=12 \\ perpendicular\left(p\right)=8 \end{gathered}$$

Step 2. Find one of the angles of a right angle triangle

Let $B$be the angle

Then$$\begin{gathered} \sin B=\frac{p}{h} \\ \sin B=\frac{8}{12}=\frac{2}{3} \\ B=41.8 \end{gathered}$$

Step 3. Find another angle in the triangle

Since the given triangle is right angle triangle,

So let $C=90$and $B=41.8$

the sum of the angle is 180

$$\begin{gathered} A+B+C=180 \\ A+41.8+90=180 \\ A=48.2 \end{gathered}$$