Rule of Cosines - Setup (Level 1)

This math topic involves using the Rule of Cosines to solve triangles, specifically focusing on the setup of the formula. It includes multiple problems where students are asked to select the correct formula to calculate a side length of a triangle given some sides and an included angle. Each problem offers multiple answer choices in the form of expressions involving the triangle's mathematical properties. This topic is part of a larger unit on solving triangles in trigonometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry - Rule of Cosines - Setup Worksheet

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Math worksheet on 'Trigonometry - Rule of Cosines - Setup (Level 1)'. Part of a broader unit on 'Trigonometry - Law of Sines, Cosines - Intro' Learn online: app.mobius.academy/math/units/trigonometry_law_of_sines_cosines_intro/
1
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 11 to the power of 2 + 7 to the power of 2 - 2 times 11 times 7 times cos(30)
b A LaTex expression showing square root of 11 to the power of 2 + 30 to the power of 2 - 2 times 11 times 30 times cos(7)
c A LaTex expression showing square root of 11 to the power of 2 + 11 to the power of 2 - 2 times 11 times 11 times cos(7)
d A LaTex expression showing square root of 11 to the power of 2 + 60 to the power of 2 - 2 times 11 times 60 times cos(30)
e A LaTex expression showing square root of 11 to the power of 2 + 7 to the power of 2 - 2 times 11 times 7 times cos(11)
2
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 8 to the power of 2 + 160 to the power of 2 - 2 times 8 times 160 times cos(80)
b A LaTex expression showing square root of 8 to the power of 2 + 11 to the power of 2 - 2 times 8 times 11 times cos(8)
c A LaTex expression showing square root of 8 to the power of 2 + 8 to the power of 2 - 2 times 8 times 8 times cos(11)
d A LaTex expression showing square root of 8 to the power of 2 + 80 to the power of 2 - 2 times 8 times 80 times cos(11)
e A LaTex expression showing square root of 8 to the power of 2 + 11 to the power of 2 - 2 times 8 times 11 times cos(80)
3
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 10 to the power of 2 + 3 to the power of 2 - 2 times 10 times 3 times cos(10)
b A LaTex expression showing square root of 10 to the power of 2 + 3 to the power of 2 - 2 times 10 times 3 times cos(35)
c A LaTex expression showing square root of 10 to the power of 2 + 10 to the power of 2 - 2 times 10 times 10 times cos(3)
d A LaTex expression showing square root of 10 to the power of 2 + 35 to the power of 2 - 2 times 10 times 35 times cos(3)
e A LaTex expression showing square root of 10 to the power of 2 + 70 to the power of 2 - 2 times 10 times 70 times cos(35)
4
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 6 to the power of 2 + 6 to the power of 2 - 2 times 6 times 6 times cos(12)
b A LaTex expression showing square root of 6 to the power of 2 + 120 to the power of 2 - 2 times 6 times 120 times cos(60)
c A LaTex expression showing square root of 6 to the power of 2 + 12 to the power of 2 - 2 times 6 times 12 times cos(6)
d A LaTex expression showing square root of 6 to the power of 2 + 12 to the power of 2 - 2 times 6 times 12 times cos(60)
e A LaTex expression showing square root of 6 to the power of 2 + 60 to the power of 2 - 2 times 6 times 60 times cos(12)
5
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 12 to the power of 2 + 55 to the power of 2 - 2 times 12 times 55 times cos(4)
b A LaTex expression showing square root of 12 to the power of 2 + 12 to the power of 2 - 2 times 12 times 12 times cos(4)
c A LaTex expression showing square root of 12 to the power of 2 + 110 to the power of 2 - 2 times 12 times 110 times cos(55)
d A LaTex expression showing square root of 12 to the power of 2 + 4 to the power of 2 - 2 times 12 times 4 times cos(12)
e A LaTex expression showing square root of 12 to the power of 2 + 4 to the power of 2 - 2 times 12 times 4 times cos(55)
6
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 9 to the power of 2 + 6 to the power of 2 - 2 times 9 times 6 times cos(80)
b A LaTex expression showing square root of 9 to the power of 2 + 9 to the power of 2 - 2 times 9 times 9 times cos(6)
c A LaTex expression showing square root of 9 to the power of 2 + 6 to the power of 2 - 2 times 9 times 6 times cos(9)
d A LaTex expression showing square root of 9 to the power of 2 + 160 to the power of 2 - 2 times 9 times 160 times cos(80)
e A LaTex expression showing square root of 9 to the power of 2 + 80 to the power of 2 - 2 times 9 times 80 times cos(6)
7
Select the right formula to calculate the side length indicated
An svg image showing a math problem
a A LaTex expression showing square root of 6 to the power of 2 + 90 to the power of 2 - 2 times 6 times 90 times cos(45)
b A LaTex expression showing square root of 6 to the power of 2 + 6 to the power of 2 - 2 times 6 times 6 times cos(7)
c A LaTex expression showing square root of 6 to the power of 2 + 45 to the power of 2 - 2 times 6 times 45 times cos(7)
d A LaTex expression showing square root of 6 to the power of 2 + 7 to the power of 2 - 2 times 6 times 7 times cos(45)
e A LaTex expression showing square root of 6 to the power of 2 + 7 to the power of 2 - 2 times 6 times 7 times cos(6)