Question

Find the length of the side AB in the triangle ABC.​

Answer 1

Answer:

220.645

Step-by-step explanation:

A trick with triangles, if two angles are given you actually know the third, because all three angles of any triangle add up to 180 degrees.  So the third, if you know two, is 180 minus the first angle and the second angle.  In this case 180-55-62 = 63 degrees

Since this problem involves two sides and you know all the angles you can use the law of sines.  The law of sines is:

$\frac{Sin(A)}{a}=\frac{Sin(B)}{b}=\frac{Sin(C)}{c}=\frac{Sin(A)}{a} or \frac{a}{Sin(A)}= \frac{b}{Sin(B)}= \frac{c}{Sin(C)}= \frac{a}{Sin(A)}$

You can use it with the sine on the top or bottom.  It doesn't matter in this case.  Also, capital letters are the angle measures and lower case letters are the side measures.  Also, important to note we only start knowing one side and angle pair, B.  b=240 and B=63 as shown above.  So keep that in mind for what to do.

We want to findside AB, or if we want it to correspond with an angle, that is side C, hopefully you see that.  It doesn't matter how you write it, unless your teacher wants a certain way, I find it easier  labeling it with one letter when possible.  Sometimes it is not possible.  

So using the law of sines we know $\frac{b}{Sin(B)}=\frac{c}{Sin(C)}$

pluging in we get

$\frac{240}{Sin(63)}=\frac{c}{Sin(55)}$

multiply both sides of the equation by Sin(55) and you'll get your answer

$Sin(55)\frac{240}{Sin(63)}$

Again, let me know if there's any confusion.