Law of Sines/Cosines Worksheets Grade 11

1. Mere is analyzing a triangular sail for a boat. The sail has sides of 44 m and 52 m, and the angle between these sides is 112°. Find the length of the third side of the sail to the nearest meter.
2. Hana is a conservation ranger monitoring a rare bird population in a triangular nature reserve. From her observation tower at point A, she spots a nesting site at point B, 14 kilometers away. She also spots a feeding ground at point C, 22 kilometers away. The angle between the lines from the tower to the nesting site and to the feeding ground is 48 degrees. To calculate the flight path distance between the nesting site and the feeding ground for her report, Hana needs to find the straight-line distance from point B to point C. What is this distance, to the nearest kilometer?
3. In triangle PQR, side p = 12, side q = 18, and angle R = 110°. Find side r using the Law of Cosines: r = ?

…and 4 more problems

1. Tane is a pilot flying a triangular search pattern over a forest. He flies from point P to point Q, a distance of 92 kilometers. He then turns and flies from point Q to point R, a distance of 64 kilometers, making an angle of 74 degrees at Q between the two legs of the flight. To complete the pattern, he needs to fly directly from R back to P. How far is the flight from R to P, to the nearest kilometer?
2. Aroha is surveying a triangular field. From a reference point, she measures two sides: one side is 93 meters long, and another side is 115 meters long. The angle between these two sides is 67 degrees. What is the length of the third side of the field, to the nearest meter?
3. sin(30°) × 8 ÷ sin(45°) = ?

…and 4 more problems

1. 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?
2. Olivia is designing a triangular hiking trail in a nature reserve. She marks two points, A and B, which are 80 meters apart along a straight path. From point A, she sights a large oak tree at point C, and measures the angle between line AB and line AC as 55 degrees. From point B, she measures the angle between line BA and line BC as 40 degrees. Olivia needs to calculate the distance from point A to the oak tree (side AC) to determine the length of the first leg of the trail. What is the distance AC, to the nearest meter?
3. Noah is an architect designing a triangular support truss for a pedestrian bridge. He knows two sides of the triangular truss measure 26 meters and 31 meters, and the angle between these two sides is 56 degrees. To order the correct length of steel for the third side, Noah needs to calculate its exact length. What is the length of the third side of the triangular truss, to the nearest meter?

…and 4 more problems