MATH SOLVE

4 months ago

Q:
# 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/nb) 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/nd) there is one possible triangle because the pattern within the given information b is side-side-angle.

Accepted Solution

A:

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:

[tex] \frac{sin M}{m} = \frac{sin N}{n} [/tex]

Let's try to solve for sin N:

sin N = [tex] \frac{n sin N}{m} [/tex]

= [tex] \frac{20 sin42}{12} [/tex]

= 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.

[tex] \frac{sin M}{m} = \frac{sin N}{n} [/tex]

Let's try to solve for sin N:

sin N = [tex] \frac{n sin N}{m} [/tex]

= [tex] \frac{20 sin42}{12} [/tex]

= 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.