Question

Find C and D using formula for special right triangles

Answer 1

Given:

Right triangles:

To find:

The value of c and value of d

Solution:

In the first right triangle:

θ = 45°

Opposite side to θ = 5

Hypotenuse = c

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

$\sin 45^\circ=\frac{5}{c}$

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

$\frac{1}{\sqrt 2}=\frac{5}{c}$

Do cross multiplication, we get

$c=5\sqrt{2}$

In the second right triangle:

θ = 60°

Opposite side to θ = 4

Adjacent side to θ = d

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

$\tan 60^\circ=\frac{4}{d}$

$\sqrt{3} =\frac{4}{d}$

Do cross multiplication, we get

$d=\frac{4}{\sqrt{3} }$

The value of $c=5\sqrt{2}$ and $d=\frac{4}{\sqrt{3} }$.