Law of Sines ApplicationsName_________________________

1. Find the height of the building in the figure below to the nearest foot.

2. Fire towers A and B are located 10 miles apart. They use the direction of the other tower as0°. Rangers at fire tower A spots a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the fire to the nearest tenth of a mile?

3. Find the height of the tree below to the nearest foot.

4. Triangulation can be used to find the location of an object by measuring the angles to the object from two points at the end of a baseline. Two lookouts 20 miles apart on the coast spot a ship at sea. Using the figure below find the distance, d, the ship is from shore to the nearest tenth of a mile.

5. Flights 104 and 217 are both approaching O’Hare International Airport from directions directly opposite one another and at an altitude of 2.5 miles. The pilot on flight 104 reports an angle of depression of 17º to the tower, and the pilot on flight 217 reports an angle of depression of 12º to the tower. Calculate the distance between the planes.

6. Hewey, Dewey, and Louie are camping in their tents. If the distance between Hewey and Dewey is 153 feet, the distance between Hewey and Louie is 201 feet, and the distance between Dewey and Louie is 175 feet, what is the angle between Hewey, Dewey, and Louie?

7. Matt measures the angle of elevation of the peak of a mountain as 35º. Susie, who is 1200 feet closer on a straight level path, measures the angle of elevation as 42º. How high is the mountain?

8. A real estate agent has just take a trigonometry class at the local community college. She is considering purchasing a piece of property and is waiting for the surveyor’s report before closing the deal. If the surveyor submits a drawing as in the figure below, explain why the agent will reject the sale.

9. State the number of possible triangles that can be formed using the given measurements. Then solve the triangle (find ALL possible solutions).

a. In ∆ STR, m∠ S=75 °, r=18 , and s=26. b. In ∆≝¿ m∠D=16 °,f=23 , and d=19.