Find the missing side and angle indicated in the picture. Round your answers to the nearest tenth. Enter your answer as equations separated by a comma.

AC = 30 in

m∠B = 36,9°

m∠A = 53,1°

Step-by-step explanation:

1 AC

You gan get AC with the pythagorean theorem:

a²+b²=c²

We are looking for side b of the triangle, so the equation is rearranged for b.

BC²+AC²=AB²    | -BC²

AC²=AB²-BC²

AC=√(AB²-BC²)

Now the given values are used:

b=√(50²-40²)

b=√(2500-1600)

b=√900

b=30 in

2 m∠B

This angle can be calculated using the sine law:

sine(angle)=opposite cathete/hypothenus

We are looking for angle m∠B of the triangle.

sin(m∠B)=AC/AB

sin(m∠B)=30in/50in

sin(m∠B)=0,6

m∠B=36,9°

3 m∠A

This angle can be calculated using the sine law:

sine(angle)=opposite cathete/hypothenus

We are looking for angle m∠A of the triangle.

sin(m∠A)=BC/AB

sin(m∠A)=40in/50in

sin(m∠A)=0,8

m∠A=53,1°