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PsychrolutesMarcidus
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

[tex] \frac{sinW}{w}= \frac{sinV}{x} [/tex]

Then simply isolate x
[tex] \frac{sinW}{w}= \frac{sinV}{x} [/tex]
[tex]x \frac{sinW}{w}= sinV[/tex]
[tex]x (sinW)= wsinV[/tex]
[tex]x =\frac{ wsinV}{sinW}[/tex]
[tex]x =\frac{ 19sin30}{sin249}[/tex]
[tex]x =\frac{9.5}{sin249}[/tex]



kudzordzifrancis
ANSWER

[tex]x = 10.2m[/tex]

EXPLANATION

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

From the ∆UVW,

[tex] \frac{x}{ \sin( 30 \degree)} = \frac{19}{ \sin( < \: UWV)} [/tex]

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

This implies that,

[tex]< \: UWV+30 \degree+81\degree=180\degree[/tex]

Group like terms and simplify to get,

[tex]< \: UWV=180\degree - 111\degree[/tex]

[tex]< \: UWV=69\degree [/tex]

[tex] \frac{x}{ \sin( 30 \degree)} = \frac{19}{ \sin( 69 \degree)} [/tex]

[tex] x = \frac{19}{ \sin( 69 \degree)} \times \sin(30 \degree) [/tex]

[tex]x = 10.2m[/tex]

to the nearest tenth.

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