Name: Carole
Level of the question: Secondary

Question: okays, well, im having difficulty finding the side of a triangle. It is a right triangle and the information given is that the hypotonous is 24 and the angle adjacent to the 90 degree is 32. Im trying to find X, which is placed on the bottom leg of the triangle, and have no idea how to do it. can you explain to me how to get the answer, please? i'd like to know for future reference, please. thank you.

Hi Carole.

When I tried drawing what you describe, I get confused because you say that the angle adjacent to the 90 degree angle is 32 degrees, but there are TWO angles adjacent to the 90 degree angle and I’m not sure if you are describing

You get different answers depending on which picture you use, but both use trigonometric functions.

In a right triangle (that’s one that has a 90 degree angle), the ratios of the sides represent different trig functions.  Let’s name the sides of the triangle as “hypotenuse” (the side opposite the right angle), “adjacent” and “opposite”.  These last two are in reference to some other angle in the triangle.

What that means is that in my left diagram, x is the adjacent side.  In my right diagram, it is the opposite side.

Now here are the three basic trig functions:

The symbol  (that’s the Greek letter “theta”) represents the angle you are using as a reference for those opposites and adjacents.  In your case,  = 32 degrees and the hypotenuse = 24 units.  You have to solve for x.

Look at the diagrams and pick the one that matches yours.  Then figure out whether you are dealing with a ratio involving the adjacent side or the opposite side.  Look at my list of trig functions and decide which one is appropriate.  Then you can solve for x and get your answer.

Hope this helps!

Stephen La Rocque>