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)

Answer 1

Check the picture below.

notice, the width is the cosine and the length is the sine.

$\bf sin(60^o )=\cfrac{y}{47}\implies 47\cdot sin(60^o)=y\implies 47\cdot \cfrac{\sqrt{3}}{2}=y \\\\\\ \cfrac{47\sqrt{3}}{2}=\stackrel{length}{y}\\\\ -------------------------------\\\\ cos(60^o )=\cfrac{x}{47}\implies 47\cdot cos(60^o)=x\implies 47\cdot \cfrac{1}{2}=x \\\\\\ \cfrac{47}{2}=\stackrel{width}{x}\\\\ -------------------------------\\\\ x\cdot y\implies \cfrac{47\sqrt{3}}{2}\cdot \cfrac{47}{2}\implies \cfrac{2209\sqrt{3}}{4}\impliedby \textit{area of the mirror}$

Answer 2

Answer:

A is correct

Step-by-step explanation: