Question

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

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

$\dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

$c = \dfrac{b \sin C}{\sin B}$

$c = \dfrac{ 91.791 \sin 31.683^\circ }{\sin 71.484 ^\circ} = 50.842$

Answer: 50.842 meters