Question

What is the value of x?

Answer 1

See Below

Explanation:

In `RST` we have `sin60=2sqrt3/h` where h is the hypotenuse of this triangle and catetus of `TRQ`

In this formula we have `sin60=sqrt3/2=2sqrt3/h` and from here

`h=4`

Now in triangle `TRQ`

`tan45=1=x/4` then `x=4`

Answer 2

Use trig ratios to calculate first the hypotenuse of triangle TSR, which is the adjacent side of triangle TRQ, and then `x`, the opposite side of triangle TRQ.

Explanation:

Use trig ratios to calculate first the hypotenuse of triangle TSR, which is the adjacent side of triangle TRQ, and then `x`, the opposite side of triangle TRQ.

`ul(RT)=(2sqrt(3))/(sin60)=4`

`ul(RQ)=4tan45=4`

Note that when we knew `ul(RT)` we already knew `ul(RQ)`, because the 45 degree angle in TRQ means that it is isosceles.