Question

Please help ASAP! Law of Sines question...

Answer 1

Answer:

$\large\boxed{a=10.92\ and\ b=14.52}$

Step-by-step explanation:

Step 1:

Calculate a measure of angle C.

We know: The sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

$m\angle C+43^o+115^o=180^o$

$m\angle C+158^o=180^o$          subtract 158° from both sides

$m\angle C=22^o$

Step 2:

Use the law of sines to calculate the length a:

$\dfrac{6}{\sin22^o}=\dfrac{a}{\sin43^o}$

$\sin22^o\approx0.3746\\\\\sin43^o\approx0.6820$

$\dfrac{6}{0.3746}=\dfrac{a}{0.6820}$          multiply both sides by 0.6820

$a\approx10.92$

Step 3:

Use the law of sines to calculate the length b:

$\dfrac{6}{\sin22^o}=\dfrac{b}{\sin115^o}$

$\sin22^o\approx0.3746$

To calculate sin115°, use the formula:

$\sin(180^o-\theta)=\sin\theta$

$\sin115^o=\sin(180^o-65^o)=\sin65^o$

$\sin65^o\approx0.9063$

$\dfrac{6}{0.3746}=\dfrac{b}{0.9063}$         multiply both sides by 0.9063

$b\approx14.52$