Please help ASAP! Law of Sines question...

Question

asked Jan 5, 2020 226k views

1 Answer

Jloubert · Answer 1 · 2020-01-10T19:20:33+0000

Answer:

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

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:

$(6)/(\sin22^o)=(a)/(\sin43^o)$

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

(6)/(0.3746)=(a)/(0.6820) multiply both sides by 0.6820

$a\approx10.92$

Step 3:

Use the law of sines to calculate the length b:

$(6)/(\sin22^o)=(b)/(\sin115^o)$

$\sin22^o\approx0.3746$

To calculate sin115°, use the formula:

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

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

$\sin65^o\approx0.9063$

(6)/(0.3746)=(b)/(0.9063) multiply both sides by 0.9063

$b\approx14.52$