Question

The Law of Cosines can be used to solve a triangle in which two sides and the included angle are known, or those in which three sides are known.

To find the distance across the lake from two camping grounds at Lake Mead, a surveyor makes the following measurements.

Use these measurements to find the distance between A and B to the nearest yard. (The picture is attached below) =)

Answer 1

We need to know the Law of Cosines to get started.

The square of one side of a triangle is equal to the sum of the squares of the other two sides of the triangle minus twice the product of those two sides and the cosine of the angle included between them.

So, applying that to this scenario,

(AB)² = 60² + 100² - 2*60*100*cos(80 degrees)

Does anyone agree that this is a correct way to get started on the problem?
@catsarecool1995

Answer 2

@catsarecool1995 Are you going to work this out?

It would begin:

(AB)² = 60² + 100² - 2*60*100*cos(80 degrees)
(AB)² = 3 600 + 10 000 - 12 000 * .174
(AB)² = ?

If you do this step, I'll compare what you get with what I get and help you get to the end of this if you want to do that. Please check my work.