Word Problems Using the Law of Sines NAME ______
PERIOD ______
Use the Law of Sines to solve the following problems. Write trig equation- show work (2 decimal places)
1) A triangular lot faces two streets that meet at an angle of 85º. The sides facing the streets are each 160 feet in length. Find the perimeter of the lot./ 2) The towns of Lansdale and Dolyestown are 12 miles apart. The angles of elevation to a hot air balloon directly between the towns are 12º and 35º respectively. How far is the balloon from Lansdale?
3) Due to prevailing winds, a tree grows so that it is leaning 6º from vertical. At a point 100 feet away from the tree, the angle of elevation to the top of the tree is 23º. Find height of the tree.
/ 4) From the parking lot at Red Hill Shopping Center, the angle of elevation to the top of the hill is 25º. From the base of the hill, the angle of elevation to the hilltop is 55º. If the distance between the sighting points is 740 feet, how high is Red Hill?
5) The angles of elevation to a plane from two observation points A and B on the ground are 51º and 68º, respectively. If points A and B are 2.5 miles apart and the plane is east of both points, find the altitude of the plane.
Use the Law of Cosines to solve the following problems. Write formula – show work (2 decimal places)
6] A pilot is flying from Chicago to Columbus, a distance of 300 miles. If he starts his trip 15º off course and flies on this course for 75 miles, how far is he from Columbus?/ 7] A ship at sea is 70 miles from one transmitter and 130 miles from another. If the transmitters are 183 miles apart, what is the measurement between the signals?
8] Two straight roads diverge at a 57º angle. If two cars leave the intersection at 2:00 P.M., one traveling at 40 mph and the other at 50 mph, at 2:30 P.M. how far apart are the cars?
/ 9]
A cable car is to be installed to the top of a mountain from a point 800 feet from its base. If the distance up the side of the mountain is 3537 feet and the angle between the ground and the mountain is 106º, what is the length of the cable?
10] A triangular field has sides with lengths 22, 36 and 44 yards. Find the largest angle.