Question 57 Answer and Explanation _ACT June 2009 Form 67C Math Section

57. Triangle △ABC is shown in the figure below. The measure of ∠A is 40°, AB = 18 cm, and AC = 12 cm. Which of the following is the length, in centimeters, of BC ?

(Note: For a triangle with sides of length a, b, and c opposite angles ∠A, ∠B, and ∠C, respectively, the law of sines states $\dfrac{\sin \angle A}{a}=\dfrac{\sin \angle B}{b}=\dfrac{\sin \angle C}{c}$ and the law of abc cosines states c² = a² + b² - 2ab cos∠C.)

A. 12 sin 40°

B. 18 sin 40°

C. $\sqrt{{18}^{2}-{12}^{2}}$

D. $\sqrt{{12}^{2}+{18}^{2}}$

E. $\sqrt{{12}^{2}+{18}^{2}-2\left({12}\right)\left({18}\right)\cos{{40}^{\circ}}}$

Answer and Explanation

Your Answer is

Correct Answer is E

Explanation