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The measures of the sides of a triangle are 10, 7, and 9. How do you find the measure of the largest angle?

1 Answer

Shwetank Mauria

Jun 25, 2016

The largest angle is ${76.226}^{o}$ $76.226^o$

Explanation:

WE use cosine law i.e. $c^{2} = a^{2} + b^{2} - 2 a b cos C$ $c^2=a^2+b^2-2abcosC$ ,

The largest angle will be opposite the largest side i.e. $10$ $10$ .

Hence $10^{2} = 7^{2} + 9^{2} - 2 \times 7 \times 9 \times cos C$ $10^2=7^2+9^2-2xx7xx9xxcosC$ or

$100 = 49 + 81 - 126 \times cos C$ $100=49+81-126xxcosC$

Hence $cos C = \frac{100 - 49 - 81}{- 126} = \frac{30}{126} = 0.2381$ $cosC=(100-49-81)/(-126)=30/126=0.2381$

Hence $∠ C = {76.226}^{o}$ $/_C=76.226^o$

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