Question

Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of angle BAC is 70.5 , and the measure of angle ACB is 38.83 . Find the distance between points A and B (to the nearest meter).A. 33 mB. 35 mC. 68 mD. 70 m

Answer 1

From the given information, the sketch of the problem is shown below:

It is required to find the distance between points A and B.

The sum of angles in a triangle is 180º, it follows that:

`\begin{gathered} A+B+C=180^(\circ) \\ \Rightarrow70.5^(\circ)+B+38.83^(\circ)=180^(\circ) \\ \Rightarrow B+109.33^(\circ)=180^(\circ) \\ \Rightarrow B=180^(\circ)-109.33^(\circ) \\ \Rightarrow B=70.67^(\circ) \end{gathered}`

Recall from the Law of Sines that the following equation holds:

`(AB)/(\sin C)=(AC)/(\sin B)`

Substitute the angle measures and side length into the equation: