Right Triangles?

Question

I have been working with finding the sides of Right Triangles given a side and an angle.

I am ok with determining what function to use though am quite confused with determining whether I should multiply or divide to get an answer?

What information is given that determines multiplication or division?

Thanks ,

Brian

Answer 1

It depends on the sides they give you.

The major formula is a^2+b^2=c^2.

a-shortest

b-mid

c-hypotenuse

α-smallest<opposite side a

β-mid " " " b

γ-rt< " " " c

For any triangle a/sinα=b/sinβ=c/sinγ.

As for a rt triangle sinγ=1.

Answer 2

Hello Brian,

I hope this can clear things up for you.

Let's call one of the non-90 degree angles A. There are three sides to the triangle, One is opposite to the angle A, one is adjacent to the angle A and, of course there is the hypotenuse, which is the side opposite the 90 degree angle.

Dealing with a right triangle there are three functions you can use.

sin(A) = opposite/hypotenuse,

cos(A) =adjacent/ hypotenuse, and

tan(A) = opposite/adjacent

Say you know the angle A and the hypotenuse and you want to know the opposite side.

The formula which has these three terms is the first one.

sin(A) = opposite/hypotenuse; sin(A) and hypotenuse, you know. Let's say A is 30 degrees and the hypotenuse is 5. The sin of 30 degrees is 0.5, so the formula becomes

0.5 = opposite / 5

Now if you multiply both sides of the equation by 5, you will have

5 * 0.5 = 5* opposite / 5

Since, on the right side of the equation you are multiplying and dividing by 5, the 5's cancel each other.

This leaves you with 2.5 = opposite.

Just choose the formula you need and substitute the numbers you know. With some practice, it will become second nature.