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.

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

50.842 meters

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation: