Lauren

It would be much easier to describe the triangle expressed in the problem statement, if it could be drawn.

In any case, the triangle discussed has 3 angles of 114 degrees (BAC), 45 degrees (ACB), and 21 degrees (ABC). (The 3rd angle of 21 degrees (for ABC) is computed as 180-114-45, since the sum of the angles in a triangle equals 180).

Also from the problem statement, the side AC (which is the side opposite to angle ABC) has a length of 45 meters.

The width of the crater being asked for is the distance from point A to point B or side AB of the triangle.

Using the law of sines:

(Sin of angle ABC)/(distance AC) = (Sin of angle ACB)/(AB)

Substituting, we have:

(Sin 21 degrees)/(45) = (Sine 45 degrees)/(AB)

Solving for AB:

AB = ((Sin 45)*(45))/(Sin 21)

AB = (.707*45)/(.358)

**AB = 88.87 meters**

I realize this is difficult to visualize without a picture. You should try drawing one out for yourself from the problem statement. Draw the crater as a circle. Then pick two points on the edge that are opposite each other and label them as A and B. Then pick a point C outside the circle which is 45 meters away from A. Draw the triangle ABC. Hopefully, you can follow the steps explained above from this picture.

Hope this helps!

George T