Question

Emilio assigns values to some of the measures of triangle MNP. if <M=42°, m=12 in., and n=20 in., which is true?

a) the triangle does not exist because sinN/n cannot equal sinM/n
b) the triangle does not exist because the pattern within the given information is side-side-angle.
c) there is one possible triangle because sinN/n can be made to equal to sinM/n
d) there is one possible triangle because the pattern within the given information b is side-side-angle.

Answer 1

A) the triangle does not exist because sinN/n cannot equal sinM/m

Explanation:

edg2020

Answer 2

You are given two sides of the triangle and one angle, opposite to one of the given sides, therefore you can try to apply the Law of sine:


`(sin M)/(m) = (sin N)/(n)`

Let's try to solve for sin N:

sin N =
`(n sin N)/(m)`
=
`(20 sin42)/(12)`
= 1.11

As you know, there is no angle whose sine is greater than 1, therefore the correct answer is: A) the triangle does not exist because sinN/n cannot equal sinM/m

NOTE: in your question this option has a typo.