Question

Eric is hanging a rectangle mirror that has a diagonal of 47 inches with an angle of depression of 60°. How many square inches is the mirror? (round to nearest tenth)
A) 956.5 in2

B) 1,104.5 in2

C) 1,365.5 in2

D) 1795.5 in2

Answer 1

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:

$\frac{a}{Sin(A)} = \frac{b}{Sin(B)} =\frac{c}{Sin(C)}$

Let's find c:

$\frac{b}{Sin(B)} =\frac{c}{Sin(C)}\\\\ \frac{47}{Sin(90)} =\frac{c}{Sin(30)}\\\\c=\frac{47sin(30)}{sin(90)} =\frac{47}{2}$

Let's find a:

$\frac{b}{Sin(B)} =\frac{a}{Sin(A)}\\\\ \frac{47}{Sin(90)} =\frac{c}{Sin(60)}\\\\c=\frac{47sin(60)}{sin(90)} =\frac{47\sqrt{3} }{2}$

Now, the area of a rectangle is the product between its base and its height:

$A=a*b=\frac{47}{2} *\frac{47\sqrt{3} }{2} =956.5250585\approx956.5in^2$

Answer 2

Answer:

It is A. 956.5 in2 this will help you