Question

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

Answer 1

To answer this question, we will use the sine law which is illustrated in the attached image.

We are given that:
The distance from school to library = a
∠A = 32
∠B = 110
b = 2.2

Substitute with the givens in the relation of the sine law to get a as follows:
(sin 32) / (a) = (sin 110) / (2.2)
a = (2.2 sin 32) / (sin 110)
distance from school to library = a = 1.2406 mi

Based on the above calculations, the best choice would be:
B. 1.2 mi

Answer 2

This can be done using the sine rule.
$\frac{sin(110)}{2.2}= \frac{sin(32)}{x}$
Where x is the distance from the school to the library.

Rearranging the formula to solve for x:
$x= \frac{2.2sin(32)}{sin(110)} =1.241$

Therefore the most appropriate answer is B - 1.2mi