Download Laws of Sines and Cosines

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Law of Sin and Cos Word Problems
Draw a picture, set up the problem, and solve. Show all of your work for full credit.
1. Points A an B are on opposite sides of the Grand Canyon. Point C is 200 yards from A. Angle B measures
87o and angle C measures 67o. What is the distance between A and B?
2. Two observers are standing on shore ½ mile apart at points A and B and measure the angle to a sailboat at
a point C at the same time. Angle A is 63o and angle B is 56o. Find the distance from each observer to the
sailboat.
3. 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 60o; to the top is 62.5o.
Determine the height of the flagpole.
4. Two sides and the included angle of a parallelogram have measures 3.2, 4.8, and 54o respectively. Find the
lengths of the diagonals.
5. 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 ft side.
6. The measures 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 at the vertices.
7. On a map, Orlando is 178 mm due south of Niagara Falls, Denver is 273 mm from Orlando, and Denver is
235 mm from Niagara Falls. Find the bearing of Denver from Orlando. Find the bearing of Denver from Niagara
Falls.
8. Dana is flying a kite whose string is 65 meters long and makes a 70º angle with the ground. How far is the
kite above the ground?
9. The top of a lighthouse is 120 meters above sea level. The angle of depression from the top of the
lighthouse to a ship is 23º. How far is the ship from the base of the lighthouse?
10. A house is built on a triangular plot of land. Two sides of the plot are 160 feet long and they meet at an
angle of 85º. If a fence is to be built around the property, how much fencing is needed?
11. The longest side of a triangle is 34’. The measures of two angles of the triangle are 40 and 65. Find the
lengths of the other two sides.
12. Two sides of a triangular plot have lengths of 400 inches and 600 inches. The angle formed by those sides
measures 46.3º. Find the perimeter of the plot to the nearest foot.
13. The measures of the sides of a triangle are 6.8, 8.4, and 4.9. Find the measure of the smallest angle to the
nearest degree.
14. The sides of a triangle are 50 meters, 70 meters and 85 meters long. Find the measure of the largest
angle to the nearest degree.
15. An isosceles triangle has a base of 22 centimeters and a vertex angle of 360. Find the perimeter of the
triangle.
16. The longest side of a triangle is 30 inches long. Two of the angles have measures of 45 and 79. Solve the
triangle.