Hello, Keith!

This problem requires the Law of Sines.

There are two forms, but one is the reciprocal of the other.

. .

Solve the triangle: .

She told us that this one has two triangles: . . . . the dreaded Ambiguous Case!

. . (34.8°, 125.2°, 7.2), (145.2°, 34.8°, 5) . . . Her second one is wrong!

I like to organize the facts in a chart.

. .

We can find angle with: .

We have: .

Hence: .or**

We will solve the triangle forbothvalues of

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[1]

Our chart looks like this:

. .

We need only side

We will use: .

We have: .

Therefore: .

And this our completed chart:

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

[2]

Our chart looks like this:

. .

We need only side

We will use: .

We have: .

Therefore: .

And this our completed chart:

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

Whenever we use , there aretwopossible answers.

Our calculator gives us only the acute angle (in Quadrant 1).

. . The other angle is its supplement (subtract from 180°).

We must be constantly alert to the possibility of a second angle.