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

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:

$\frac{sin M}{m} = \frac{sin N}{n}$

Let's try to solve for sin N:

sin N = $\frac{n sin N}{m}$
         = $\frac{20 sin42}{12}$
         = 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.

Answer 2

Answer:

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

Step-by-step explanation:

edg2020