Question 42 Answer and Explanation _ACT December 2022 Form F07 Math Section

42. The diagram below shows the location of Manuel’s boat, which is on a lake and anchored to a stationary buoy at point B. On the shore, Manuel’s house is at point H and his nearest neighbor’s house is at point N, which is 150 meters from H. The measures of 2 angles are given. Which of the following expressions represents the straight-line distance, in meters, from B to N ?

(Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively,

F. $\frac{150\,sin\,{50}^{\circ}}{sin\,{60}^{\circ}}$

G. $\frac{150\,sin\,{50}^{\circ}}{sin\,{70}^{\circ}}$

H. $\frac{150\,sin\,{60}^{\circ}}{sin\,{50}^{\circ}}$

J. $\frac{150\,sin\,{60}^{\circ}}{sin\,{70}^{\circ}}$

K. $\frac{150\,sin\,{70}^{\circ}}{sin\,{50}^{\circ}}$

Answer and Explanation

Your Answer is

Correct Answer is G

Explanation

∠B=180-50-60=70°, according to the sine law, sin70°/150=sin50°/? , the calculated value is 150sin50°/sin70°, choose G