Question

Which proportion could be used to find the length of side b?

Answer 1

Answer: A for Apex.

Explanation:

Answer 2

A)
`(sin(23))/(6.2)=(sin(85))/(b)`

Explanation:

In order to use the Law of Sines, we must have a known angle and the known side opposite it.

The only side measure we have is that of AB, which is 6.2. The angle opposite this is ∠C, which we do not have the measurement of.

We do have the measurement of ∠A and ∠B; we can use these to find the measure of ∠C. We know that the sum of the measures of the angles in a triangle is 180°; this means

m∠C = 180-(72+85) = 180-157 = 23°

This makes the first ratio in the Law of Sines

`(sin(23))/(6.2)`

We are trying to find the measure of b. This means we use the angle opposite b, ∠B; m∠B = 85°. This gives us the ratio

`(sin(85))/(b)`

Together, this gives us the proportion

`(sin(23))/(6.2)=(sin(85))/(b)`