Law of Sines/Cosines Worksheets Grade 11

1. Matiu is designing a triangular garden bed. He knows two sides of the triangular bed are 24 meters and 18 meters long, and the angle between these two sides is 68 degrees. To purchase enough edging for the third side, he needs to calculate its length. What is the length of the third side, to the nearest meter?
2. In triangle ABC, side a = 15, side b = 20, and angle C = 60°. Find side c using the Law of Cosines: c = ?
3. In triangle ABC, side a = 20, side b = 25, and angle C = 120°. Find side c using the Law of Cosines.

…and 5 more problems

1. Noah is designing a triangular support frame for a sculpture. He has two steel beams measuring 21 meters and 16 meters, which he plans to join at an angle of 71 degrees. To complete the triangle, he needs to cut a third beam to connect the free ends of the two beams. What is the length of the third beam, to the nearest meter?
2. Aroha is a landscape architect designing a triangular pond feature in a city park. She knows two sides of the triangular pond are 47 meters and 33 meters long, and the angle between these two sides is 51 degrees. To order the appropriate length of decorative border for the third side, she needs to calculate its length. What is the length of the third side, to the nearest meter?
3. Hana is a surveyor mapping a triangular plot of land for a new community garden. She measures two sides of the triangle: one side is 42 meters long, and another side is 31 meters long. The angle between these two sides is 74 degrees. To complete her map, Hana needs to find the length of the third side of the triangle. What is the length of the third side, to the nearest meter?

…and 4 more problems

1. Mason is a marine archaeologist mapping a submerged triangular artifact site near a coral reef. Using sonar from his boat at point A, he measures the distance to a large rock formation at point B as 92 meters. He then travels to point C and measures the distance from point C back to the boat at point A as 64 meters. The angle at point A between the lines to points B and C is 54°. Mason needs to know the straight-line distance between the rock formation at point B and point C to complete his site map. What is the distance between points B and C, to the nearest meter?
2. Mason is surveying a triangular piece of land for a construction project. He measures two sides of the triangle: one side is 18 meters long, another side is 24 meters long, and the angle opposite the 18-meter side is 35 degrees. Determine the length of the third side to the nearest meter.
3. sin(45°) × √2 = ?

…and 3 more problems