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=(5)/(c)`

The value of sin 45° =
`(1)/(\sqrt 2)`

`$(1)/(\sqrt 2)=(5)/(c)`

Do cross multiplication, we get

`c=5√(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=(4)/(d)`

`$√(3) =(4)/(d)`

Do cross multiplication, we get

`$d=(4)/(√(3) )`

The value of
`c=5√(2)` and
`d=(4)/(√(3) )`.