Question

The measures of three parts of ΔABC are given in the diagram. What is AC, correct to two decimal places?

Answer 1

we know that

In the triangle ABC

Applying the law of sines

 $\frac{AB}{sinC}= \frac{AC}{sinB}$

we have

$AB=3.61\ units$

$C=41.82\°$

$B=67.62\°$    

substitute the values

 $\frac{3.61}{sin(41.82\°)}= \frac{AC}{sin(67.62\°)}$

$AC=\frac{3.61}{sin(41.82\°)}{sin(67.62\°)}$

$AC=5.01\ units$

therefore

the answer is

$AC=5.01\ units$

Answer 2

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle.

Hence

sin 41.82 / 3.61 = sin 67.62 / AC

0.66679 / 3.61 = 0.92467 / AC

0.1847 = 0.92467 / AC

AC = 0.92467 / 0.1847

AC = 5.006 = 5.01