Question

The red line in the figure is an altitude of triangle LMN. Using right angle trigonometry, write an equation involving sinN.

Answer 1

sin(N) = a/b

Explanation:

I would use the formula "sin = opposite/hypotenuse".

This formula comes from the math concept of "soh cah toa".

The only important info we need is that MN is the hypotenuse and that N(is the reference angle).

If N is the reference angle, the segment directly across is opposite which is ML.

So, so far...

MN = hypotenuse

N = reference angle

ML(y) = opposite

which means...

LN(b) = adjacent.

Sin(N) = opposite/hyptoentuse

Let's check out the 1st option:

ML(y) = opposite (correct) bc it corresponds to the correct Sin(N) format.

a = hypotenuse (incorrect) bc the hypotenuse is across from the right angle. plus it wouldn't match up with ML(y) being the opposite.

So, no to Option 1.

Let's check out the 2nd option:

a = opposite (correct) bc it corresponds to the correct Sin(N) format.

ML(y) = hypotenuse (incorrect bc LN(b) would be the hypotenuse)
So, not to Opition 2.

Let's Check out 3rd option:

b = opposite (incorrect) bc it would be the hypotenuse.

a = hypotenuse (incorrect) bc it would be the opposite.

So, not to Option 3.

Let's Check out the 4th option:

a = opposite (correct) bc it's the segment right across from the reference angle N.

b = hypotenuse (correct) because it's across from the right angle.)

Yes to option 4!

Answer 2

sin N =
`(a)/(b)`

Explanation:

the altitude of a triangle is at right angles to MN

thus Δ LMN is divided into 2 right triangles

using the right triangle on the right with hypotenuse b , then

sin N =
`(opposite)/(hypotenuse)` =
`(a)/(b)`