Math Analysis
Law of Sines and Cosines Packet
Name:
1. Two large screen televisions are suspended high from a ceiling in a mall. From a point on the floor a
distance of d1 and d2 can be computed, the distances along the floor to directly under the TV’s. Using
surveyor’s instruments, two lines of sight, one to each television can be created and the angles
between them can be gathered. Using the diagram and the given information, compute the distance D
between the two tv’s.
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𝛼 = 25°
𝛽 = 30°
𝜃 = 35°
𝑑1 = 139𝑓𝑡
𝑑2 = 153 𝑓𝑡
2. A reconnaissance plane patrolling at 5000 ft sights a submarine at a bearing of N35oE and at an angle
of depression of 25o. The same plane also spots a carrier ship at a bearing of N105oE and at an angle
of depression of 60o. If the sub were to launch a torpedo that travels at 100 ft per second, how long
before it reaches the carrier?
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3. A park ranger establishes an observation post from which to watch for poachers. Despite losing her
map, the ranger does have a compass and a range finder. She observes some poachers and the range
finder indicates that they are 500 feet from her position. They are headed toward big game that she
knows to be 375 ft from her position. Using her compass, she finds that the poachers’ azimuth (angle
measure from North) is 355o and that of the big game is 42o. What is the distance between the
poachers and the game?
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4. A bridge is being built across a canyon. The length of the bridge is 5045 ft. From the deepest point in
the canyon, the angles of elevation to the ends of the bridge are 78o and 72o. How deep is the canyon?
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5. A batter in a baseball game drops a bunt down the first base line. It rolls 34 feet at an angle of 25o with
the base path. The pitcher’s mound is 60.5 feet from home plate. How far must the pitcher travel to
pick up the ball? (Hint: A baseball diamond is a square)
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6. Two ships leave harbor at the same time. The first sails N 15o W at 25 knots, and the second sails
N32oE at 20 knots. After 2 hours, how far apart are the ships? (Hint: a knot is 1 nautical mile per hour)
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7. The coast guard stations at Summerville Pier and Hamlin Beach are 23 miles apart. Hamlin is due
west of Summerville. Both stations simultaneously observe a damsel in distress aboard the “Oasis”
stranded in Lake Ontario. From Summerville the bearing to the Oasis is N26o15’W and from Hamlin
it is N39o45’E. Find the distance of the Oasis from Hamlin and Summerville.
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8. On a beautiful day, Captain Addy spotted a stranded motor boat in the middle of Lake Ontario. She
calculated that the bearing to the motor boat to be N63o12’E. At the same time a fishing vessel named
“The Elliott” spotted the same boat at a bearing of N15o20’W. Captain Addy calculated the The Elliott
was 12 miles away from her position. She also noted that the bearing to the Elliott was S51o25’E.
a. How far was the motor boat from the Elliott?
b. How far was the motor boat from Captain Addy?
c. What was the bearing from the motor boat to Captain Addy?
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9. A boat is sailing due east, parallel to the shoreline at a speed of 10 nautical miles per hour. At a given
time, the bearing to a lighthouse located on the shoreline is S 72o E, and 15 minutes later, the bearing
is S 66o E. Find the shortest distance from the boat to the shoreline at the current position.
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