Name__________________________________
Applications
Law of Sines/Cosines
For each word problem, draw a picture, write an equation and solve each problem. Make sure you
label your solution answering the question being asked.
(1) Brianna is taking a walk along a straight road. She decides to leave the road, so she walks on a path
that makes an anlge of 35° with the road. After walking for 450 meters, she turns 75° and heads back
towards the road.
(A) How far does Brianna need to walk on her current path to get back to the road?
(B) When Brianna returns to the road, how far along the road is she from where she started?
(2)A rock climber is part of the way up a climb when he can see both the peak and the base of the Gray
Mountain. When viewing the peak of the mountain, his angle of elevation is 42°. When viewing the
base of the mountain, his angle of depression is 36°. If he knows the Gray Mountain is 2000 feet high
and the base of the mountain is at sea level, then what is the elevation of the climber to the nearest
foot?
(3) Two radar stations 2.4 miles apart are tracking an airplane. The straight-line distance between
station A and the plane is 7.4 miles. The straight-line distance between station B and the plane is 6.9
miles. What is the angle of elevation from station A to the plane? Round to the nearest degree.
(4) A fishing pole is resting against the railing of a boat making an angle of 22° with the boat’s deck. The
fishing pole is 5 feet long, and the hook hangs 3 feet from the tip of the pole. The movement of the
boat causes the hook to sway back and forth. Determine which angles the finishing line must make
with the pole in order for the hook to be level with the boat’s deck.
(5) Gina’s handheld computer can send and receive emails if it is within 40 miles of a transmission tower.
On a trip, Gina drives past the transmission tower on Highway 7 for 32 miles, and then she turns 97
degrees onto Oakville Road and drives for another 19 miles.
(A) Is Gina close enough to the transmission tower to be able to send and receive emails?
Explain your reasoning.
(B) If Gina is within range of the tower, how much can she drive on Oakville Road before she is out of
range? If she is out of range and drives back towards Highway 7, how far will she travel before she is
back in range?
(6) During a figure skating routine, Jackie and Peter skate apart with an angle of 15° between them.
Jackie skates for 5 meters and Peter skates for 7 meters. How far apart are the skaters?
(7) A person at A looks due east and sees a UFO with an angle of elevation of 40°. At the same instant,
another person, 1.0 miles due west of A looks due east and sights the same UFO with an angle of
elevation of 25°. Find the distance between A and the UFO. How far is the UFO above the ground?
(8) A vertical flagpole is attached to the top edge of a building. A man stands 400 feet from the base of
the building. From his viewpoint, the angle of elevation to the bottom of the flagpole is 60°; to the top is
62.5°. Determine the height of the flagpole.
(9) When a boy stands on the bank of a river and looks to the other bank, the angle of depression is 12°.
If he climbs to the top of a 10 ft. tree and looks across to the other bank, the angle of depression is 15°.
What is the distance from the first position of the boy to the other bank of the river? How wide is the
river?
(10) On a baseball diamond with 90-foot sides, the pitcher’s mound is 60.5 feet from home plate. How
far is the pitcher’s mound from third base?
(11) The measure of two sides of a parallelogram are 28 in. and 42 in. If the longer diagonal has
measure 58 in., find the measures of the angles of the vertices.
(12) A bridge is supported by triangular braces. If the sides of each brace have lengths 63 feet, 46 feet,
and 40 feet, find the measure of the angle opposite the 46 foot side.
(13) On a map, Orlando is 178mm due south of Niagara Falls, Denver is 273 mm from Orlando, and
Denver is 235 mm from Niagara Falls. Find the bearing(Direction) of Denver from Orlando? Find the
bearing of Denver from Niagara Falls.