Question

in exercises 5–7, find the values of x and y. write your answers in simplest form.
5.
6.
7.

Explanation:

Exercise 5

Step1: Find hypotenuse $y$

$\sin(30^\circ)=\frac{15}{y} \implies y=\frac{15}{\sin(30^\circ)}=\frac{15}{\frac{1}{2}}=30$

Step2: Find adjacent side $x$

$\tan(30^\circ)=\frac{15}{x} \implies x=\frac{15}{\tan(30^\circ)}=\frac{15}{\frac{1}{\sqrt{3}}}=15\sqrt{3}$

Exercise 6

Step1: Find side $y$ (adjacent to 60°)

$\cos(60^\circ)=\frac{y}{22} \implies y=22\times\cos(60^\circ)=22\times\frac{1}{2}=11$

Step2: Find side $x$ (opposite to 60°)

$\sin(60^\circ)=\frac{x}{22} \implies x=22\times\sin(60^\circ)=22\times\frac{\sqrt{3}}{2}=11\sqrt{3}$

Exercise 7

Step1: Find hypotenuse $y$

$\cos(30^\circ)=\frac{9}{y} \implies y=\frac{9}{\cos(30^\circ)}=\frac{9}{\frac{\sqrt{3}}{2}}=6\sqrt{3}$

Step2: Find side $x$ (opposite to 30°)

$\tan(30^\circ)=\frac{x}{9} \implies x=9\times\tan(30^\circ)=9\times\frac{1}{\sqrt{3}}=3\sqrt{3}$

Answer:

Exercise 5: $x=15\sqrt{3}$, $y=30$
Exercise 6: $x=11\sqrt{3}$, $y=11$
Exercise 7: $x=3\sqrt{3}$, $y=6\sqrt{3}$