Question

#5 - find the values of x and y. Write your answers in simplest form.

Answer 1

Given:

In the given triangle,

With respect to 30°, the perpendicular = 9, the base = x and the hypotenuse = y

To find the value of x and y.

Formula

By Trigonometric ratio we get,

$sin\theta = \frac{opposite}{Hypotenuse}$ and

$tan\theta =$ $\frac{opposite}{adjacent}$

Now,

Putting, perpendicular = 9 and $\theta=30^\circ$ we get,

$sin30^\circ = \frac{9}{y}$

or, $\frac{1}{2} = \frac{9}{y}$

or, $y =18$ [ by cross multiplication]

Again,

$tan30^\theta = \frac{9}{x}$

or, $\frac{1}{\sqrt{3} } = \frac{9}{x}$

or, $x = 9\sqrt{3}$ [ by cross multiplication]

Hence,

The value of x and y is 9√3 unit and 18 unit respectively.