Question 59 Answer and Explanation _ACT December 2018 Form B05 Math Section

59. Jed is standing 10 meters from a maple tree that is 14 meters from a willow tree, as shown in the figure below, in which the measure of an angle is given. Which of the following equations, when solved for x, gives the distance, x meters, between Jed and the willow tree?

(Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A，∠B, and ∠C, respectively, c² = a² + b² -2ab cos∠C )

A. ${10}^{2}={x}^{2}+{14}^{2}-2x(14)(\cos{{34}^{\circ}})$

B. ${10}^{2}={x}^{2}+{14}^{2}-2(10)(14)(\cos{{34}^{\circ}})$

C. ${14}^{2}={x}^{2}+{10}^{2}-2x(14)(\cos{{34}^{\circ}})$

D. ${x}^{2}={10}^{2}+{14}^{2}-2x(14)(\cos{{34}^{\circ}})$

E. ${x}^{2}={10}^{2}+{14}^{2}-2(10)(14)\cos{{34}^{\circ}}$

Answer and Explanation

Your Answer is

Correct Answer is A

Explanation

Just set the formula, c is 10