Question

What is the value of x?

Answer 1

ANSWER

$x = 10.2m$

EXPLANATION

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

From the ∆UVW,

$\frac{x}{ \sin( 30 \degree)} = \frac{19}{ \sin( < \: UWV)}$

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,

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

$< \: UWV=69\degree$

$\frac{x}{ \sin( 30 \degree)} = \frac{19}{ \sin( 69 \degree)}$

$x = \frac{19}{ \sin( 69 \degree)} \times \sin(30 \degree)$

$x = 10.2m$

to the nearest tenth.

Answer 2

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

$\frac{sinW}{w}= \frac{sinV}{x}$

Then simply isolate x
$\frac{sinW}{w}= \frac{sinV}{x}$
$x \frac{sinW}{w}= sinV$
$x (sinW)= wsinV$
$x =\frac{ wsinV}{sinW}$
$x =\frac{ 19sin30}{sin249}$
$x =\frac{9.5}{sin249}$