Question 35 Answer and Explanation _ACT OG2 Form 2MC Math Section

35. A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 2 vessels is 5°. The approximate distance, in miles, from the cargo ship to the fishing boat is given by which of the following expressions ?

(Note: The law of cosines states that for any triangle with vertices A, B, and C and the sides opposite those vertices with lengths a, b, and c, respectively, c² = a² + b² - 2ab cos C.)

A. $\sqrt{{(5.0)}^{2}-{(4.2)}^{2}}$

B. $\sqrt{{(4.2)}^{2}+{(5.0)}^{2}-2\cdot4.2\cdot5.0\,cos\,{5}^{\circ}}$

C. $\sqrt{{(4.2)}^{2}+{(5.0)}^{2}+2\cdot4.2\cdot5.0\,cos\,{5}^{\circ}}$

D. $\sqrt{{(4.2)}^{2}+{(5.0)}^{2}-2\cdot4.2\cdot5.0\,cos\,{85}^{\circ}}$

E. $\sqrt{{(4.2)}^{2}+{(5.0)}^{2}+2\cdot4.2\cdot5.0\,cos\,{85}^{\circ}}$

Answer and Explanation

Your Answer is

Correct Answer is B

Explanation

The formula of the cosine theorem is given in the article, and a and b in the cosine theorem are assigned as 4.2 and 5 respectively, and c is the unknown side ∠C is 5 degrees, so choose B