Section 7.7Law of Cosines

Law of Cosines• How can I apply the Law of Cosines?

Law of Cosines

A

a

B

b

C

c

Law of Cosines

• Memory aid: the angle must match with the side you are solving for

Example of finding a side• Find each measure using the given measures from

ABC. Round angle measures to the nearest degree and sides to the nearest tenth.

• If b = 14, c = 12, and mA = 62, find a.

• If a = 20, c = 25 and mB = 82, find b. 

Example of finding an angle• Find each measure using the given measures from

ABC. Round angle measures to the nearest degree and sides to the nearest tenth.

• If a = 11, b = 10 and c = 12, find mB.

• If a = 24, b = 18, and c = 16, find mC.

Given all three sides• In ∆LMN, l = 24, m = 27 and n = 5, find m.

Homework• Section 7.7• Page 388• 11 – 18

• Study Guide and Review• Page 393• 9, 10, 14, 17, 19, 23, 24, 25, 27, 30

Which Law?• How can I solve non-right triangles using the Law

of Sines and Law of Cosines?

Law of Sines• Used in 2 cases:• Know 2 angles and any side (AAS or ASA)• Know 2 sides and an angle opposite one of the sides (SSA)

Law of Cosines• Used in 2 cases:• Know all three sides (SSS)• Know two sides and the included angle (SAS)

• *Don’t forget the sum of angles is 180°

Solve each ∆LMN• m = 44, l = 54, mL=23

• m = 19, n = 28, mL=49

• mM = 46, mL = 55, n = 16

• n = 17, m = 20, l = 14

Homework• Page 388• 19 – 25• 41 and 42

• Fill in Chapter 7 Example chart

Lesson Plan• Intro

• Previously we did the Law of Sines, today is the Law of Cosines.

• Standards-• Supplies – slides, whiteboard, Timing - 2 days. The second

day is figuring out which law to utilize.• Day 1

• Essential Questions- slide 2• Input – slides 3 and 4• Guided Practice – slides 5 and 6• Independent Practice – Bookwork

• Day 2• Essential Question - 9• Input – slide 10 & 11• Guided Practice – slide 12• Independent Practice - Bookwork