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
[tex]$\sin \theta=\frac{\text { Opposite side of } \theta}{\text { Hypotenuse }}[/tex]
[tex]$\sin 45^\circ=\frac{5}{c}[/tex]
The value of sin 45° = [tex]\frac{1}{\sqrt 2}[/tex]
[tex]$\frac{1}{\sqrt 2}=\frac{5}{c}[/tex]
Do cross multiplication, we get
[tex]c=5\sqrt{2}[/tex]
In the second right triangle:
θ = 60°
Opposite side to θ = 4
Adjacent side to θ = d
[tex]$\tan \theta=\frac{\text { Opposite side of } \theta}{\text { Adjacent side of } \theta}[/tex]
[tex]$\tan 60^\circ=\frac{4}{d}[/tex]
[tex]$\sqrt{3} =\frac{4}{d}[/tex]
Do cross multiplication, we get
[tex]$d=\frac{4}{\sqrt{3} }[/tex]
The value of [tex]c=5\sqrt{2}[/tex] and [tex]d=\frac{4}{\sqrt{3} }[/tex].
