Answer:
A) 956.5 in2
Explanation:
First, take a look a the picture I attached you... As you can see, using the information provided by the problem, we can deduce two values, the value of the B angle and the value of the C angle. B is 90 because is a right angle, and C is 30 because the sum of the interior angles of a triangle is equal to 180, so:
90+60+C=180
Solving for C:
C=180-90-60=30.
Now, we need to use this information in order to find a and c which are the height and the base respectively. There a couple of ways to solve this. I will use Law of Sines:
[tex]\frac{a}{Sin(A)} = \frac{b}{Sin(B)} =\frac{c}{Sin(C)}[/tex]
Let's find c:
[tex]\frac{b}{Sin(B)} =\frac{c}{Sin(C)}\\\\ \frac{47}{Sin(90)} =\frac{c}{Sin(30)}\\\\c=\frac{47sin(30)}{sin(90)} =\frac{47}{2}[/tex]
Let's find a:
[tex]\frac{b}{Sin(B)} =\frac{a}{Sin(A)}\\\\ \frac{47}{Sin(90)} =\frac{c}{Sin(60)}\\\\c=\frac{47sin(60)}{sin(90)} =\frac{47\sqrt{3} }{2}[/tex]
Now, the area of a rectangle is the product between its base and its height:
[tex]A=a*b=\frac{47}{2} *\frac{47\sqrt{3} }{2} =956.5250585\approx956.5in^2[/tex]
