Given:
θ = 60°
Opposite side of θ = 6
Adjacent side of θ = x
Hypotenuse = y
To find:
The value of x and y.
Solution:
Using basic trigonometric ratio formula:
[tex]$\tan\theta =\frac{\text{Opposite side of } \theta}{\text{Adjacent side of } \theta}[/tex]
[tex]$\tan60^\circ=\frac{6}{x}[/tex]
The value of tan 60° = √3
[tex]$\sqrt{3} =\frac{6}{x}[/tex]
Multiply by x on both sides.
[tex]$\sqrt{3} \times x=\frac{6}{x} \times x[/tex]
[tex]$\sqrt{3} \times x=6[/tex]
Divide by √3 on both sides, we get
[tex]$\frac{\sqrt{3} \times x}{\sqrt{3} } =\frac{6}{\sqrt{3} }[/tex]
[tex]x=2\sqrt{3}[/tex]
Using Pythagoras theorem:
[tex]\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2[/tex]
[tex]y^2 = 6^2 +({2\sqrt {3}})^2[/tex]
[tex]y^2 = 36 +12[/tex]
[tex]y^2 = 48[/tex]
Taking square root on both sides, we get
[tex]y=4 \sqrt{3}[/tex]
Therefore, the exact values of x and y are [tex]x=2 \sqrt{3}, y=4 \sqrt{3}[/tex].
