Precalculus 3421 Name Unit 7 Law of Sines and Law of Cosines Date Per

Precalculus 3421 Name ________________________

Unit 7 Law of Sines and Law of Cosines Date _____Per _______

LT 7.2 I can use the Laws of Sines and Cosines to model and solve real-life problems.

Worksheet 1
1. The distance on a map from the airport in Miami, FL to the one in Nassau, Bahamas is 295 kilometers due east. Bangor, Maine is northeast of both cities; its airport is 2350 kilometers from Miami and 2323 kilometers from Nassau. What bearing would a plane need to fly from Nassau to Bangor?

(Bearing is the degree from straight north).

2. You are heading to Beech Mountain for a ski trip. Unfortunately, state road 105 in North Carolina is blocked off due to a chemical spill. You have to get to Tynecastle Highway which leads to the resort at which you are staying. NC-105 would get you to Tynecastle Hwy in 12.8 miles. The detour begins with a 18^o veer off onto a road that runs through the local city. After 6 miles, there is another turn that leads to Tynecastle Hwy. Assuming that both roads on the detour are straight, how many extra miles are you traveling to reach your destination?

3. From a certain distance the angle of elevation to the top of a building is 17^o. At a point 50 meters closer to the building, the angle of elevation is 31^o. Approximate the height of the building.

4. Two motorists start at the same point and travel in two straight courses. The courses diverge by 95^o. If one is traveling at 50 mph and the other is traveling at 65 mph, how far apart will they be after 4 hours?

5. In problem 4, when will they be 400 miles apart?

6. Two Coast Guard Stations are on a north-south line 65 miles apart. The northernmost station hears an SOS distress call on a bearing of S43^oE and the southern station hears the same distress call on a bearing of N56^oE. How far must the helicopter from the southern station fly to reach the troubled ship?

7. Ally the surveyor must find the distance from A and B on opposite sides of a lake. She locates point C that is 860 ft from A and 175 ft from B. She measures o. Find the distance AB.

8. Two ranger stations are on an east-west line 110 miles apart. A forest fire is located between the two stations. From the western station, the fire is at an angle of elevation of 48^o . From the eastern station, the angle of elevation is 75^o. How far is the fire from the western station?

9. The lengths of the diagonals of a parallelogram are 10 feet and 16 feet. Find the lengths of the sides od the parallelogram if the diagonals intersect at an angle of 28^o.