Question

Find the missing side length of X

Answer 1

Alright, lets get started.

Please refer the diagram I have attached.

In the lower triangle, two angles are given as 60° and 90°.

The third angle could be find by subtracting these two angle from 180°. (Because the sum of angles of a triangle is 180°)

So, the third angle would be =
`180 - 60 - 90`

Third angle would be = 30°

Now we could use SOH CAH TOA to find the side.

SOH means

`sin 30 = (opposite)/(hypotenuse)`

Hypotenuse is given as 9√6 and opposite is x

we need to find x

`sin 30 = (x)/(9√(6))`

Putting the value of sin 30 as
`(1)/(2)`

`(1)/(2) = (x)/(9√(6))`

Cross multiplying

`x = (9√(6))/(2)`

`x = 4.5√(6)` : Answer

Hope it will help :)