Question

Points A and B are on opposite sides of a lake. A point C is 91.791 meters from

a. The measure of ∠BAC ∠ B A C is 76.833°, and the measure of ∠ACB ∠ A C B is determined to be 31.683°. Find the distance between points A and
b.

Answer 1

We're given two angles and an included side and we want to solve for a side opposite one of the given angles. Using the typical triangle notation we have

b=AC=91.791 meters

A=76.833 degrees

C=31.683 degrees

and our task is to find c=AB.

To apply the Law of Sines we need B, which we get since the triangle angles add to 180 degrees:

B = 180 - A - C = 180 - 76.833 - 31.683 = 71.484 degrees

Now the Law of Sines says

`(b)/(\sin B) = (c)/(\sin C)`

`c = (b \sin C)/(\sin B)`

`c = ( 91.791 \sin 31.683^\circ )/(\sin 71.484 ^\circ) = 50.842`

Answer: 50.842 meters