Download 10.2 Law of Sines and Right Triangle Applications

10.2 Law of Sines and Right Triangle Applications Worksheet
For each problem, on a separate sheet of paper,
a) Draw a sketch
b) Write an equation and show any necessary work. Answers only receive no credit
c) Round answers to the nearest tenth.
1. Two angles of a triangle measure 32 and 53 . The longest side is 55 cm. Find the length of the
shortest side.
2. From a hang glider approaching a 5000 ft clearing the angles of depression of the opposite ends
of the field measure 24 and 30 . How far is the hang glider from the nearer end of the field?
3. A fire is sighted from two ranger stations that are 5000 m apart. The angles of observation to the
fire measure 52  from one station and 41 from the other station. Find the distance along the line
of sight to the fire from the closer of the two stations.
4. Two cables of length 300 m and 270 m extend from the top of a television antenna to the level
ground on opposite sides of the antenna. The longer cable makes an angle of 48 with the
ground. Find the acute angle that the shorter cable makes with the ground and the distance
between the cables along the ground.
5. The captain of a freighter 6 km from the nearer of two unloading docks on the shore finds that the
angle between the lines of sight to the two docks is 35 . If the docks are 10 km apart, how far is
the tanker from the farther dock?
6. Courtney places her surveyor’s telescope on the top of a tripod 5 feet above the ground. She
measures an 8 elevation above the horizontal to the top of a tree that is 120 feet away. How tall is
the tree?
7. A 75 foot long conveyor is used at the Bernard Farm to put hay bales up for winter storage. The
conveyor is tilted to an angle of elevation of 22 .
a. To what height can the hay be moved?
b. If the conveyor is repositioned to an angle of 27, to what height can the hay be
moved?
8. A vertical television mast is mounted on the roof of a building. From a point 750 ft from the base
of the building, the angles of elevation to the bottom and top of the mast measure 34 and 50
respectively. How tall is the mast?
9. Two light houses A and B are known to be exactly 20 miles apart on a north-south line. A ship’s
captain at S measures ASB to be 33 . A radio operator at B measures ABS to be 52 . Find
the distance from the ship to each lighthouse.
10. From the top of an office building 72 ft high, the angle of elevation to the top of an apartment
building across the street is 31 . From the base of the office building, the angle of elevation is
46 . How tall is the apartment building?