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4 years ago

Use the law of cosines to solve for the measure of the largest angle in triangle ABC.

Mathematics

2 answers:

marta [7]4 years ago

6 0

AB is the longest side, so ∠C is the largest angle.
use law of cosine: 16²=9²+12²-2*9*12cosC
216cosC=81+144-256=-31
cosC=-0.14352
C≈98

Anton [14]4 years ago

6 0

Answer:

The measure of the largest angle in ΔABC = 98°

Step-by-step explanation:

The longest side in the given ΔABC is AB

And, The angle opposite to the longest side is largest

⇒ ∠C is the largest angle. in the ΔABC

So, we need to find the measure of ∠C

Now, Using law of cosine in the given ΔABC :

⇒ 16² = 9² + 12² - 2 × 9 × 12·cos C

⇒ 216·cos C = 81 + 144 - 256

⇒ 216·cos C = -31

⇒ cos C = -0.14352

⇒ m∠C ≈ 98°

Hence, The measure of the largest angle in ΔABC = 98°

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