Question

Find the exact values of x and y.

Answer 1

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:

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

$\tan60^\circ=\frac{6}{x}$

The value of tan 60° = √3

$\sqrt{3} =\frac{6}{x}$

Multiply by x on both sides.

$\sqrt{3} \times x=\frac{6}{x} \times x$

$\sqrt{3} \times x=6$

Divide by √3 on both sides, we get

$\frac{\sqrt{3} \times x}{\sqrt{3} } =\frac{6}{\sqrt{3} }$

$x=2\sqrt{3}$

Using Pythagoras theorem:

$\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2$

$y^2 = 6^2 +({2\sqrt {3}})^2$

$y^2 = 36 +12$

$y^2 = 48$

Taking square root on both sides, we get

$y=4 \sqrt{3}$

Therefore, the exact values of x and y are $x=2 \sqrt{3}, y=4 \sqrt{3}$.