10 - The Cosine Law - Notes PDF

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10 - The Cosine Law

MPM2D – Trigonometry

Date: ________________________________________________

The Cosi sine ne Law

In ∆ABD: 



ℎ =! −# !()* =

In ∆ACD: ℎ  = $  − %& − # '



+ ,

Therefore: $  − %& − # ' = !  − # 

& = $  + !  − 2$!%!().'

$ = &  + !  − 2&!%!()*' !  = & + $  − 2&$ %!()/ '

In general, to use the Sine Law, we need a side and an angle across from it. We use the Cosine Law, when we are given: 1. two sides and the contained angle, or 2. three sides

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10 - The Cosine Law

MPM2D – Trigonometry

Solution to our original problem: Determine the length of side c.

Determine the measure of angle A:

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10 - The Cosine Law

MPM2D – Trigonometry

Homework 1. Given 0 = 18, 2 = 15, and ∠5 = 46°, find x. 2. Two sides of a triangle are 18 and 23 with and angle of 60° in between. How long is the third side? 3. Given & = 5, $ = 6, and ! = 7, find ∠.. 4. Find the perimeter of ΔSAT if ∠: = 56°, & = 14 and ; = 25. 5. Two roads diverge at a 52° angle. Two bikers ride away at 17 km/h and 24 km/h. How far apart are they after 2 hours? 6. Find the measure of the smallest angle in a triangle with side lengths 4, 7 and 8. 7. A clock has a 30 cm minute hand and a 20 cm hour hand. How far apart are the tips of the hands at: a. 2:00

b. 4:00

c. 5:00

b. 43.6 cm

c. 48.4 cm

Answers 1. # = 13.2 2. 21.0 3. ∠. = 44.4° 4. 59.7 5. 38.1 km or 74.0 km 6. 30° 7. a. 26.5 cm

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