Question 51 Answer and Explanation _ACT December 2015 Form 72E Math Section

51. Melanie is standing 80 feet from the launch site of a hot-air balloon when the balloon lifts off from the ground and rises vertically. Melanie’s horizontal line of sight is 5 feet above the ground. When the bottom of the balloon is 50 feet above the ground, as shown below, which of the following expressions gives the angle that Melanie’s horizontal line of sight makes with her line of sight to the bottom of the balloon?

A. ${tan}^{-1}(\frac{45}{80})$

B. ${tan}^{-1}(\frac{50}{75})$

C. ${tan}^{-1}(\frac{75}{50})$

D. ${tan}^{-1}(\frac{80}{45})$

E. ${tan}^{-1}(\frac{80}{50})$

Answer and Explanation

Your Answer is

Correct Answer is A

Explanation

Note that tan^-1=arctan here is not cot. In addition, the length of the opposite side needs to be subtracted from the person's height, which is 5 feet.