2-24 Honors Geometry Warm-up Two weather observation stations are 7 miles apart. A weather balloon is located between the stations. From Station 1, the angle of elevation to the weather balloon is 33o. From Station 2, the angle of elevation to the balloon is 52o. Find the altitude of the balloon to the nearest tenth of a mile.

7-5 Enrichment Answers: 7-6 Enrichment Answers:

7-6 Law of Sines Can be used to find missing parts in any triangle, not just right triangles!

Proof: Law of Sines sin 𝐵= ℎ 𝑎 sin 𝐴= ℎ 𝑏 𝑏 sin 𝐴=ℎ 𝑎 sin 𝐵=ℎ

Example 1A: Find d. Round to the nearest tenth. 8 17o 29o

Example 1B: Find 𝑚∠𝐿 to the nearest degree in ∆𝐿𝑀𝑁 if n=7, l=9, and 𝑚∠𝑁=43°.

Find the measures of all the angles and sides of a triangle Solving a triangle Find the measures of all the angles and sides of a triangle Example 2: Solve ∆𝐼𝐽𝐾 if 𝑚∠𝐽=32°, 𝑖=30, 𝑎𝑛𝑑 𝑗=16. Partner A: Find 𝑚∠𝐼. Partner B: Find 𝑚∠𝐾. Partner B/C: Find k.

Example 3: A civil engineer wants to determine the distances from points A and B to an inaccessible point C in a river. ∠𝐵𝐴𝐶 measures 67o and ∠𝐴𝐵𝐶 measures 52o. If points A and B are 82 feet apart, find the distance from C to each point. Partner B/C: Draw a picture. Partner B: Show what you are trying to find and explain a strategy. Partner A: Solve the problem. Get group member’s okay.

Chapter 5 Test: Find x

When can we use the Law of Sines to solve a triangle? CASE 1: You know the measures of two angles and any side of a triangle. (AAS or ASA) CASE 2: You know the measures of two sides and an angle opposite one of these sides of the triangle. (SSA)