The Law of Sines is a fundamental concept in trigonometry that allows us to solve triangles that are not right-angled. This law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides of the triangle. This worksheet will help you practice applying the Law of Sines to solve various problems involving triangles.
Before attempting the worksheet, make sure you have a solid understanding of the Law of Sines and how it can be used to solve triangles. You should also be familiar with the sine function and how to calculate the sine of an angle using a scientific calculator.
Worksheet Questions
1. In triangle ABC, angle A measures 45 degrees, side AB measures 8 units, and side BC measures 10 units. Calculate the length of side AC.
2. Triangle XYZ has angle X measuring 30 degrees, angle Y measuring 60 degrees, and side XY measuring 6 units. Calculate the length of side YZ.
3. In triangle PQR, angle Q measures 70 degrees, side PR measures 12 units, and side PQ measures 8 units. Calculate the length of side QR.
4. Triangle DEF has angle D measuring 40 degrees, angle E measuring 70 degrees, and side DE measuring 5 units. Calculate the length of side EF.
5. In triangle UVW, angle V measures 50 degrees, side UW measures 15 units, and side VW measures 12 units. Calculate the length of side UV.
6. Triangle LMN has angle L measuring 80 degrees, angle M measuring 50 degrees, and side MN measuring 7 units. Calculate the length of side NL.
7. In triangle GHI, angle H measures 60 degrees, side GI measures 9 units, and side GH measures 6 units. Calculate the length of side HI.
8. Triangle STU has angle S measuring 35 degrees, angle T measuring 55 degrees, and side ST measuring 10 units. Calculate the length of side TU.
9. In triangle JKL, angle K measures 75 degrees, side JL measures 11 units, and side JK measures 9 units. Calculate the length of side KL.
10. Triangle OPQ has angle O measuring 25 degrees, angle P measuring 85 degrees, and side PQ measuring 13 units. Calculate the length of side OQ.
These questions will test your understanding of the Law of Sines and help you practice applying it to solve triangles. Work through each question carefully and make sure to show all your workings.