Question 35 Answer and Explanation _ACT December 2010 Form 62E Math Section

35. A surveyor is going to approximate the longest distance across Lake McLeland. She finds the approximate distances, in kilometers, and the approximate angle measures, in degrees, as shown in the figure below. If RT represents the longest distance across the lake, which of the following expressions approximates the length, in kilometers, of RT ?

(Note: The law of cosines states that c²= a²+ b²- 2ab cos ∠C, where a, b, and c are the lengths of the sides of any triangle and ∠C is opposite the side of length c.)

A. $\sqrt{{31}^{2}+{36}^{2}}$

B. $\sqrt{{31}^{2}+{36}^{2}-2(31)(36)\,cos\,{47}^{\circ}}$

C. $\sqrt{{31}^{2}+{36}^{2}-2(31)(36)\,cos\,{60}^{\circ}}$

D. $\sqrt{{31}^{2}+{36}^{2}-2(31)(36)\,cos\,{73}^{\circ}}$

E. $\sqrt{{31}^{2}+{36}^{2}-2(31)(36)\,cos\,{107}^{\circ}}$

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

∠S=180-60-47=73, choose D