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Find the exact value of cos∠QPR

What is the answer to this? I'm pretty sure that I need to use law of cosines. I need all work shown and the answer.

Find the exact value of cos∠QPR What is the answer to this? I'm pretty sure that I-example-1
User Beyazid
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1 Answer

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Explanation:

since you know already that you need the law of cosine (which is nothing else than the generalization of Pythagoras from right-angled triangles to general triangles), why don't you just apply it ?

the law of cosine :

c² = a² + b² - 2ab×cos(C)

c is the side opposite of angle C, a and b are the other 2 sides.

our angle C is here now the angle QPR. the opposite side is QR = 3.

so, we have

3² = 2² + 4² - 2×2×4×cos(QPR) = 4 + 16 - 16×cos(QPR)

9 = 20 - 16×cos(QPR)

-11 = -16×cos(QPR)

cos(QPR) = -11/-16 = 11/16 = 0.6875

FYI : that means

angle QPR = 46.56746344...°

User WaLinke
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