Download Name:______________________________________________________ Date:__________________ Period:__________

Name:______________________________________________________
Date:__________________
Period:__________
Chapter 10: Applying Trig Functions
Topic 1: Law of Cosines
The law of cosines is a reference-sheet formula used to solve for missing sides or angles of a triangle.
 Similar to the _______________________________ ______________________.
 We use the law of cosines when we ______ __________ have a right triangle.
The Law of Cosines is for
Law of Cosines formulas
Recall from Geometry: Sides are named by a lower-case letter which
matches the angle is it __________________ ____________. Label the sides.
Look for “book ends”
Whether the unknown is a side or an angle, it must be either the beginning or end of the formula
Follow the pattern to fill in the rest.
Working with the formula & your calculator.
 First, always, draw & label a triangle.
 Take inventory of what you know and what you want to know (3 sides 1 angle: Law of Cosines)
 Rewrite the reference sheet formula specific to your question, starting with the bookends.
 Careful calculator work.
Examples:
1. Find x to the nearest tenth:
Name:______________________________________________________
Date:__________________
Period:__________
2. Find e to the nearest tenth:
3. In
, if
4. In
, if
, find z to the nearest unit.
, find the measure of angle A to the nearest minute.
Name:______________________________________________________
Date:__________________
Period:__________
Classwork
1. In triangle HAT, a = 6.4, t = 10.2, and m<H = 87. Find the length of side h to the nearest tenth.
2. The base angles of isosceles triangle GHI measure 54.7° while equal sides GH and HI measure 8.94 inches.
Find the length of GI to the nearest hundredth.
3. In triangle ABC, side b = 12, side c = 20 and m<A = 45. Find side a to the nearest tenth.
4. Find the largest angle, to the nearest tenth of a degree, of a triangle whose sides are 9, 12, and 18.
Name:______________________________________________________
Date:__________________
Period:__________
5. A surveyor at point R sights two points S and T on opposite sides of a lake. Point R is 120m from S and
180m from T, and the measure of <R is 38o. Find the distance across the lake to the nearest meter.
6. In a rhombus with a side of 24, the longer diagonal is 36. Find, to the nearest tenth of a degree, the larger
angle of the rhombus.
7. Three sides of a triangle measure 20, 30, and 40. Find the measure of the largest angle of a triangle to the
nearest degree.
8. The Horticulture Club is designing a wildflower garden. They want to make it in the shape of a triangle
whose sides have lengths 12 feet, 14 feet, and 18 feet. What is the measure of the smallest angle in the
triangle to the nearest degree?
Name:______________________________________________________
Date:__________________
Answer Key:
1.) 11.8
2.) 10.33
3.) 14.3
4.) 117.3
5.) 113
6.) 97.2
7.) 104
8.) 42
Period:__________