Question

Find the value of each variable. Write your answers in simplest form.

Answer 1

Answer:

$q = 16 \sqrt{2}$ and $r = 16$

Step-by-step explanation:

We know that

• $\sin( \alpha ) = \frac{side \: opposite \: to \: \alpha }{hypotenuse \: of \: triangle}$
• $\cos( \alpha ) = \frac{side \: adjacent \: to \: \alpha }{hypotenuse \: of \: traingle}$
• $\tan( \alpha ) = \frac{side \: opposite \: to \: \alpha }{side \: adjacent \: to \: \alpha }$

where $\alpha$ is an angle of a triangle.

In the triangle given above , $\alpha = 45°$. So,

1) $\sin( 45) = \frac{16}{q}$

$= > \frac{1}{ \sqrt{2} } = \frac{16}{q}$

$= > q = 16 \sqrt{2}$

2) $\tan(45) = \frac{16}{r}$

$= > 1 = \frac{16}{r}$

$= > r = 16$