EXPLANATION
If a triangle has vertices A,B and C with the given measures:
The draw is as follows:
The length of AB is given by the Pythagorean Theorem as shown as follows:
[tex]\text{Hypotenuse}^2=32.6^2+39.8^2^{}[/tex]
Computing the powers:
[tex]\text{Hypotenuse}^2=1062.76+1584.04[/tex]
Adding both numbers:
[tex]Hypoten\nu se^2=2646.8[/tex]
Applying the square root to both sides:
[tex]\text{Hypotenuse}=\sqrt[]{2646.8}[/tex]
Simplifying:
[tex]\text{Hypotenuse}=AB=51.44\operatorname{cm}[/tex]
The degree measure of [tex]\frac{\sin A}{A}=\frac{\sin B}{B}[/tex]Substituting terms:
[tex]\frac{\sin 93}{AB}=\frac{\sin A}{39.8}[/tex]
Multiplying both sides by 39.8 and substituting terms:
[tex]39.8\cdot\frac{\sin 93}{51.44}=\sin A[/tex]
Multiplying numbers:
[tex]0.77\cdot\sin 93=\sin A[/tex]
Simpifying:
[tex]0.77\cdot0.99=0.77=\sin A[/tex]
Applying sin-1 to both sides:
[tex]\sin ^{-1}(0.77)=A[/tex]
Switching sides:
[tex]A=50.25\degree[/tex]
Then, by applying the Sum of Interior Angles of a Triangle Theorem, we know that the sum of interior angles is equal to 180 degrees,thus:
[tex]180-50.25-93=B=36.75\degree[/tex]
Hence,
1) AB= 51.44 cm
2) A= 50.25°
3) B= 36.75°
