Question 55 Answer and Explanation _ACT June 2020 Form C02 Math Section

55. A 6-foot awning that extended 2 feet horizontally from a vertical building at 8:00 a.m. was adjusted to extend 3 feet horizontally from the building at 12:00 p.m., as shown below. Which of the following expressions equals the positive difference in the measures equals the positive difference in the measures of the angle between the awning and the building at 8:00 a.m.and at 12:00 p.m.?

A. ${cos}^{-1}(\frac{3-2}{6})$

B. ${sin}^{-1}(\frac{3-2}{6})$

C. ${tan}^{-1}(\frac{3-2}{6})$

D. ${cos}^{-1}(\frac{3}{6})-{cos}^{-1}(\frac{2}{6})$

E. ${sin}^{-1}(\frac{3}{6})-{sin}^{-1}(\frac{2}{6})$

Answer and Explanation

Your Answer is

Correct Answer is E

Explanation

Set the angle between the vertical vertical line and the oblique line in the first figure as x, sinx=2/6, find x=sin-1(2/6); set the angle between the vertical line and the oblique line in the second figure The included angle is y, siny=3/6, find y=sin-1(3/6); the difference between the two angles is sin-1(3/6)-x=sin-1(2/6)