Question

Given the diagram shown below, which of the following best represents the distance from the school to the library?

A. 0.8 mi
B. 1.2 mi
C. 1.6 mi
D. 2.4 mi

Answer 1

Use the sine theorem:

sin(angle A) / length of side a = sin (angle B) / lenght of side b

Here:

angle A = 32°

length of side a = length from school to library = x

angle B = 110°

length of side b = 2.2 mi

Then, sin(32°) / x = sin(110°) / 2.2 mi

=> x = 2.2 mi * sin (32) / sin (110)

x = 1.24 mi

Therefore the answer is the option B. 1.2 mi