Question

What is the value of x?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answer 1

I'll start with the obvious, all angles in a triangle add to 180°

∠uwv=360- 81-30 = 249°

Then we can find the sine law to calculate x


`(sinW)/(w)= (sinV)/(x)`

Then simply isolate x

`(sinW)/(w)= (sinV)/(x)`

`x (sinW)/(w)= sinV`

`x (sinW)= wsinV`

`x =( wsinV)/(sinW)`

`x =( 19sin30)/(sin249)`

`x =(9.5)/(sin249)`

Answer 2

ANSWER


`x = 10.2m`

Step-by-step explanation

We can use the sine rule to find the value of x.

From the ∆UVW,


`(x)/( \sin( 30 \degree)) = (19)/( \sin( < \: UWV))`

The sum of the interior angles of a triangle is 180°.

This implies that,


`< \: UWV+30 \degree+81\degree=180\degree`

Group like terms and simplify to get,


`< \: UWV=180\degree - 111\degree`


`< \: UWV=69\degree`


`(x)/( \sin( 30 \degree)) = (19)/( \sin( 69 \degree))`


`x = (19)/( \sin( 69 \degree)) * \sin(30 \degree)`


`x = 10.2m`

to the nearest tenth.