Question

Analyze the diagram below and complete the instructions that follow.

find sin
1. 1/4

2. 1/3

3. 3/5

4. 4/5

Answer 1

Answer: Choice C) 3/5

Angle NOM, or angle O for short if you just focus on triangle NOM (ignore point L), has the side MN = 3 opposite this reference angle. The hypotenuse is MO = 5 units. This is found through the pythagorean theorem

a^2+b^2 = c^2

3^2+4^2 = c^2

25 = c^2

c^2 = 25

c = sqrt(25)

c = 5

Triangle NOM is a 3-4-5 right triangle. The ratio of the opposite and hypotenuse will get us the sine of angle NOM

so,

sin(angle NOM) = opposite/hypotenuse

sin(angle NOM) = MN/MO

sin(angle NOM) = 3/5

note: we do not use point L at all, nor do we use the fact that LM = 12 To avoid potential confusion, it might be best to draw out triangle NOM only with the proper labels as you see in the diagram below (see attached image).