Law of Sines/Cosines Word Problems
PreCalculus
Name: ___________________________________________
Use the Law of Sines, Law of Cosines and Area formulas to solve the following word problems. Round all
answers to two decimal places.
1. A triangle has sides of length 5, 8, and 10. What is the measure of the largest angle?
2. To determine the distance between two aircraft, a tracking station continuously determines the distance to
each aircraft and the angle between them in relation to the tracking station. Determine the distance
between the planes when the angle between them is 42°, and the distance from the tracking station to each
plane is 35 miles and 20 miles.
3. Determine the angle θ in the design of the streetlight shown in the figure.
4. The leaning tower of Pisa is 58.36 meters tall and leans 5.36° off center, away from the building’s shadow.
When the angle of elevation to the sun is 32°, how long is it’s shadow?
5. A triangular parcel of land has borders of lengths 60 meters, 70 meters, and 82 meters. A) Find the area of
the parcel of land. B) If the land is worth $85 per square meter, what is the value of the land?
6. The baseball player in center field is playing approximately 330 feet from the television camera that is
behind home plate. A batter hits a fly ball that goes to the wall 420 feet from the camera (see figure). The
camera turns 8° to follow the play. Approximately how far does the center fielder have to run the make the
catch?
7. A 100-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the horizontal (see
figure). Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from
the base of the tower.
8. Observers at points A and B, 30 km apart, sight an airplane at angles of elevation of 40 and 75, respectively.
How far is the plane from each observer?