Let's look at a word problem which uses the Law of Sines.

For example, Jacob and Natalie are

standing on a river bank at points A and B respectively.

Natalie is 130 meters from a house located across the river at point

C. Suppose the angle A is 40 degrees and the angle B is 60 degrees.

How far are Jacob and Natalie standing from one another?

So this situation is shown here in this figure.

And remember, we label the sides

opposite the angles with the same letter but just lower case.

And since we're looking for how far apart

Jacob and Natalie are standing from one another,

that means we're looking for little c,

which is across from capital C. And this over here is little b and this is little a.

Well since we want to find little c,

we need to know capital C in order to apply the Law of Sines.

First, since the sum of the angle measures in a triangle is 180 degrees.

We have the following,

the capital C is equal to 180 degrees minus A plus B,

or C is equal to 180 degrees minus 40 degrees plus 60 degrees.

And 40 degrees plus 60 degrees is 100 degrees,

which means C is equal to 180 minus 100 or 80 degrees.

And now, we know capital A, little a,

and capital C, which means we can find little c by using the Law of Sines,

namely sine of C divided by

little c is equal to sine of A divided by little a,

or sine of 80 degrees divided by

little c is equal to sine of 40 degrees divided by 130.

Which means cross multiplying,

we get 130 times sine of

80 degrees is equal to C times sine of 40 degrees.

And now dividing both sides by sine of 40 degrees is that it's C is equal to

130 times sine of 80 degrees divided by sine of 40 degrees.

And using our calculator,

we get that this is approximately 199.2 meters.

So Jacob and Natalie are standing approximately 199.2 meters apart.

And this is an example of how we can use the Law of Sines to solve a word problem.

Thank you and we'll see you next time.