Question 49 Answer and Explanation _ACT December 2017 Form A10 Math Section

Question 49 Answer and Explanation _ACT December 2017 Form A10 Math Section

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49. The triangle shown below has side lengths 37, 38, and 39 inches. Which of the following expressions gives the measure of the largest angle of the triangle?

(Note: For every triangle with sides of length a, b, and c that are opposite ∠A, ∠B, ∠C, respectively, ${c}^{2}={a}^{2}+{b}^{2}-2ab\,cos\,C.$ )

A. ${cos}^{-1}\left({-\frac{{37}^{2}-{38}^{2}-{39}^{2}}{2\left({38}\right)\left({39}\right)}}\right)$

B. ${cos}^{-1}\left({-\frac{{39}^{2}-{37}^{2}-{38}^{2}}{2\left({37}\right)\left({38}\right)}}\right)$

C. ${cos}^{-1}\left({{37}^{2}-{38}^{2}-{39}^{2}+2\left({38}\right)\left({39}\right)}\right)$

D. ${cos}^{-1}\left({{38}^{2}-{37}^{2}-{39}^{2}+2\left({37}\right)\left({39}\right)}\right)$

E. ${cos}^{-1}\left({{39}^{2}-{37}^{2}-{38}^{2}+2\left({37}\right)\left({38}\right)}\right)$

Answer and Explanation

Your Answer is

Correct Answer is B

Explanation