Answer:
A=52.8 miles (approximately)
Step-by-step explanation:
We can assume that this triangle is not a right angle, therefore we cannot use Pythagorean theorem. Let's use the Law of Sines:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Where A is unknown, a=28 miles, b=32 miles, B=87°
Therefore by law of sines we have:
[tex]\frac{sin(A)}{28} =\frac{sin(87)}{32} \\[/tex]
By multiplying 28 to Isolate sin(A) we have:
[tex]sin(A)=\frac{28*sin(87)}{32}[/tex]
To cancel out sine on the right, we must multiply both by the inverse sine and so:
[tex]A=sin^{-1}(\frac{28*sin(87)}{32})=52.7658\\ \\A=52.8mi[/tex]
