Points A and B are in opposite sides of a lunar crater. Point C is 45 meters from point A. The measure if angle BAC is 114 degrees and the measure of angle ACB is 45 degrees. What is the width of the crater. round to the nearest hundredth

Hi Lauren,

This one is a bit hard to explain without drawing a diagram, but the law of sines states that, for a triangle, the sine of one angle divided by the length of the side opposite that angle is equal to the sine of any other angle divided by the length of the side opposite that angle.

For this problem, you must first solve the measure of angle ABC by the formula:

For this problem, you must first solve the measure of angle ABC by the formula:

180 degrees (always the sum of the three angles of a triangle)-114 degrees (angle BAC)-45 degrees (angle ACB)= 21 degrees

*(it may be helpful to draw yourself a diagram here)...*

So the solution then becomes sin(21

^{o})/45=sin(45^{o})/xDoing some basic algebra and rounding to the nearest hundredth, we arrive at

x=88.79 meters

Let me know if any of this is not clear; I hope it helps!

Jason

EDIT: Here is a rough sketch of the problem to help you visualize it better (sorry the formatting is a bit off!):

C

/ \

/ 45

^{o}\ 45m / \

/ \

/ 114

^{o}21^{o}\ /________________\

A X B