Topics
8. Right Triangles & Trigonometry
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United States of AmericaTennessee
Geometry

8.08 Law of cosines

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Which of the following is true for the given triangle?

A triangle has its sides labeled as  a,  b, and  c. The angle labeled as $\theta$θ, denoted by a green arc, is opposite side a and adjacent to sides b and c.

$\cos\theta=\frac{a^2+c^2-b^2}{2bc}$cosθ=a2+c2−b22bc​

A

$\cos\theta=\frac{b^2+a^2-c^2}{2bc}$cosθ=b2+a2−c22bc​

B

$\cos\theta=\frac{b^2+c^2-a^2}{2ab}$cosθ=b2+c2−a22ab​

C

$\cos\theta=\frac{b^2+c^2-a^2}{2bc}$cosθ=b2+c2−a22bc​

D
Easy
< 1min

To use the law of cosines to find the length of $AC$AC, which angle would need to be given?

Easy
< 1min

Find the length of $a$a using the law of cosines.

Round your answer to two decimal places.

Easy
3min

Find the length of $a$a using the law of cosines.

Round your answer to two decimal places.

Easy
2min
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Outcomes

G.N.Q.A.1

Use units as a way to understand real-world problems.*

G.N.Q.A.1.A

Use appropriate quantities in formulas, converting units as necessary.

G.SRT.C.5

Solve triangles.*

G.SRT.C.5.C

Use the Law of Sines and Law of Cosines to solve non-right triangles in a real-world context.

G.MP1

Make sense of problems and persevere in solving them.

G.MP2

Reason abstractly and quantitatively.

G.MP3

Construct viable arguments and critique the reasoning of others.

G.MP4

Model with mathematics.

G.MP5

Use appropriate tools strategically.

G.MP6

Attend to precision.

G.MP7

Look for and make use of structure.

G.MP8

Look for and express regularity in repeated reasoning.

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