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:

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

$\tan 45^\circ =\frac{16}{r}$

The value of tan 45° = 1

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

Do cross multiplication, we get

r = 16

Using trigonometric ratio formula:

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

$\sin 45^\circ =\frac{16}{q}$

The value of sin 45° = $\frac{1}{\sqrt{2} }$.

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

Do cross multiplication, we get

$q=16\sqrt{2}$

The value of r is 16 and the value of q is $16 \sqrt{2}$.