Download Apps of Law of Sines - Spokane Public Schools

Algebra 2
Name_________________________Per:_____
Trig Applications Using Law of Sines and Cosines 2015
For each problem, draw a diagram, set up the problem and solve showing all work.
1. A draftsman drew to scale a map of a development that includes a triangular playground with
sides of length 75 yd., 85 yd., and 100 yd.
a. On the map, what are the sizes of the angles of the playground?
b. What is the area of the playground?
2. If a baseball diamond is a square 90 ft. on each side and if the pitchers’ mound is 60 ft 6 in.
from home plate on the line connecting home plate with second base, how far is the
pitcher’s mound from the other three bases? (Pitcher’s mound is not at the center of diamond).
3. A vertical antenna is mounted on top of a building. From a point 40 ft. from the base of a
building, the angles of elevation of the roof and the antenna are 34° and 50° respectively.
How tall is the antenna?
4. Find the perimeter of a regular pentagon inscribed in a circle of 12 in. radius.
5. The lengths of the diagonals of a parallelogram are 84 cm and 52 cm. If the diagonals
intersect at an angle of 40°, how long are both sides of the parallelogram?
6. A tree stands vertically on a slope that is inclined with a measure of 10° with the horizontal.
When the angle of elevation of the sun measures 25°, the shadow of the tree down the
slope is 40 ft. long. How tall is the tree?
7. The straight road from Westville to Centerville is 10 mi. long and the straight road from
Centerville to Eastville is 15 mi. long. The two roads meet at an angle of 126°. The local
phone company wants to lay a phone cable that will connect Westville and Eastville directly.
a. How long should the cable be?
b. What angle will the cable make with the road from Eastville to Centerville?
8. A surveying crew is given the job of measuring the height of a mountain. From a point on
level ground, they measure an angle of elevation to the top of 21.5°. They move 507 m
closer and measure an angle of elevation of 35.7°. How high is the mountain?
9.
As Arnie Astronaut approaches two satellites, he finds that one of them is 8 km from him
and the other is 11 km. The angle between the two satellites (with Arnie at the vertex) is
120°. How far apart are the satellites?
10. Suppose you are the pilot of a commercial airliner. You find it necessary to detour around a
group of thunderclouds. You turn at an angle of 21° to your original path, fly for a while,
turn and intercept your original path at an angle of 35°, 70 km from where you left it.
How much further did you have to go because of this detour?
21°
35°
11. An oil well is to be located on a hillside that slopes at 10°. The desired rock formation has a
dip of 27° to the horizontal in the same direction as the hill slope. The well is located
3200 ft. downhill from the nearest edge of the outcropping rock formation. How deep
will the driller have to go to reach the top of the formation?
3200 ft.
Rock
12. A field has the shape of a quadrilateral that is NOT a rectangle. Three sides measure 50, 60,
and 70 m. Two angles measure 127° and 132°. Find the length of the fourth side and the
two missing angles.
60 m
127°
50 m
132°
70 m
Trig Applications Using Law of Sines and Cosines. Name__________________________Per: _______
Show diagram and work for each problem in the corresponding cell.
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