Laws of Sines and Cosines Sections 6 1

Laws of Sines and Cosines Sections 6. 1 and 6. 2

Objectives • Apply the law of sines to determine the lengths of side and measures of angle of a triangle. • Solve word problems requiring the law of sines. • Apply the law of cosines to determine the lengths of side and measures of angle of a triangle. • Solve word problems requiring the law of cosines. • Solve a word problem requiring Heron's formula.

Formulas • Law of sines • Law of cosines • Heron’s formula

Law of Sines

Law of Cosines

Use the Law of Sines to find the value of the side x.

Use the Law of Cosines to find the value of the side x. x

Two ships leave a harbor at the same time, traveling on courses that have an angle of 140 degrees between them. If the first ship travels at 26 miles per hour and the second ship travels at 34 miles per hour, how far apart are the two ships after 3 hours?

The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 48 miles apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87 degrees and 84 degrees. How far is the satellite from station A? How far is the satellite above the ground?

A triangular parcel of land has sides of length 680 feet, 320 feet, and 802 feet. What is the area of the parcel of land? If land is valued at $2100 per acre (1 acre is 43560 square feet), what is the value of the parcel of land. Heron’s Formula