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Lesson 12.3 Law of Cosines
Name: _______________________
Period: ____________
Show all of your work.
Date: ___________
1. Solve for the variable.
a. b2 = 142 + 292 – 2(14)(29)cos123.5o
b. 3.82 = 4.02 + 5.12 – 2(4.0)(5.1)cosC
2. Use the given values to write an equation for the unknown measure. Then solve the
equation. Round to the nearest tenth.
a. b = 9, c= 12, A = 110o, a = _____
b. a = 5, b = 3, c = 4, A = _____
c. a = 3.5, b = 6.9, C = 82.5o, c = _____
3. State what method you would use to solve each problem.
a. A right triangle with given the lengths of two sides, find the length of the third side.
b. A right triangle with one side, one acute angle, find the length of the other sides
c. Given the measures of two angles of a triangle and the length of one of the sides that is
not between them, find the length of one of the other two sides
d. Given the lengths of all three sides of a triangle, find the measure of the smallest angle.
e. A right triangle with three side lengths given, find the measure of the acute angles.
4. Find unknown angle measures and side lengths. Round to the nearest tenth.
5. Use the Law of Cosines to find the measure of the largest angle of a triangular garden
whose sides measure 12.5 ft, 19.8 ft, and 15.7 ft.