Answer:
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°
