Question

How to get these variables?

Answer 1

Given:

Right triangle with one angle 45°

To find:

The value of q and r.

Solution:

Opposite to θ = 16

Adjacent to θ = r

Hypotenuse = q

Using trigonometric ratio formula:

`$\tan \theta =\frac{\text{Opposite side to } \theta}{\text{Adjacent to } \theta}`

`$\tan 45^\circ =(16)/(r)`

The value of tan 45° = 1

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

Do cross multiplication, we get

r = 16

Using trigonometric ratio formula:

`$\sin \theta =\frac{\text{Opposite side to } \theta}{\text{Hypotenuse}}`

`$\sin 45^\circ =(16)/(q)`

The value of sin 45° =
`(1)/(√(2) )`.

`$(1)/(√(2) ) =(16)/(q)`

Do cross multiplication, we get

`q=16√(2)`

The value of r is 16 and the value of q is
`16 √(2)`.