Question

Find the value of x and y. Write your answers in simplest form.

Answer 1

`x = (16√(3))/(3)`

`y = (32\sqrt 3)/(3)`

Explanation:

Calculating (x):

Here, we make use of the tan formula

`tan\theta = (Opp)/(Adj)`

Where

`\theta = 60`

`Opp = 16`

`Adj = x`

This gives:

`tan\ 60= (16)/(x)`

Make x the subject

`x = (16)/(tan\ 60)`

tan(60) in surd form is
`√(3)`

So:

`x = (16)/(√(3))`

Rationalize

`x = (16)/(√(3)) * (√(3))/(√(3))`

`x = (16√(3))/(3)`

Calculating (y):

Here, we make use of the tan formula

`sin\theta = (Opp)/(Hyp)`

Where

`\theta = 60`

`Opp = 16`

`Hyp= y`

This gives:

`sin\ 60= (16)/(y)`

Make y the subject

`y= (16)/(sin\ 60)`

tan(60) in surd form is
`(√(3))/(2)`

`y= (16)/((√(3))/(2))`

`y = 16/(\sqrt 3)/(2)`

`y = 16*(2)/(\sqrt 3)`

`y = (32)/(\sqrt 3)`

Rationalize

`y = (32)/(\sqrt 3)*(\sqrt 3)/(\sqrt 3)`

`y = (32\sqrt 3)/(3)`