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8.06 Law of cosines

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+c2b22bc

A

$\cos\theta=\frac{b^2+a^2-c^2}{2bc}$cosθ=b2+a2c22bc

B

$\cos\theta=\frac{b^2+c^2-a^2}{2ab}$cosθ=b2+c2a22ab

C

$\cos\theta=\frac{b^2+c^2-a^2}{2bc}$cosθ=b2+c2a22bc

D
Medium
< 1min

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

Medium
< 1min

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

Round your answer to two decimal places.

Medium
3min

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

Round your answer to two decimal places.

Medium
2min
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Outcomes

G.SRT.D.10 (+)

Prove the laws of sines and cosines and use them to solve problems.

G.SRT.D.11 (+)

Understand and apply the law of sines and the law of cosines to find unknown measurements in right and non-right triangles.

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