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 = (opposite)/(Hypotenuse)` and

`tan\theta =`
`(opposite)/(adjacent)`

Now,

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

`sin30^\circ = (9)/(y)`

or,
`(1)/(2) = (9)/(y)`

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

Again,

`tan30^\theta = (9)/(x)`

or,
`(1)/(√(3) ) = (9)/(x)`

or,
`x = 9√(3)` [ by cross multiplication]

Hence,

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