Question

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

Answer 1

`q = 16 √(2)` and
`r = 16`

Explanation:

We know that

• 
  `\sin( \alpha ) = (side \: opposite \: to \: \alpha )/(hypotenuse \: of \: triangle)`
• 
  `\cos( \alpha ) = (side \: adjacent \: to \: \alpha )/(hypotenuse \: of \: traingle)`
• 
  `\tan( \alpha ) = (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) = (16)/(q)`

`= > (1)/( √(2) ) = (16)/(q)`

`= > q = 16 √(2)`

2)
`\tan(45) = (16)/(r)`

`= > 1 = (16)/(r)`

`= > r = 16`