Expert: Ahmed Salami - 11/24/2011

Question
Dear Ahmed,

I'm in 6th grade and having some trouble with a trig problem(s) I was wondering if you could list the steps to solving these problems. I've tried every search engine, and it brought back no results. The first problem says SOLVE FOR x.

THe diagram is a right triangle with 2 given angles. Ninety degrees and 81 degrees. Angle O is 81 degrees and Angle M is 90 degrees. X is the side between M and O. The side opposite and O is 63 in. SO, basically i need to know the adjacent side. The hypotenuse is not given. I cant figure a way out to find the hypotenuse without using the pythagorean theorem, which requires bot the opposite and adjacent sides, which I cannot do becuase there is no adjacent length given. Please the the steps and maybe the solution to check my work,  and compare answers. Thanks.

Answer
Hi Haley,
Have you tried using the trigonometric method for an angle in a right triangle?
A way to always remember it is the mnemonic SOHCAHTOA which stands for;
S ine = O pposite/H ypothenuse
C osine = A djacent/H ypothenuse
T angent = O pposite/A djacent

And in this situation we could write
tan 81° = 63/x
x = 63/tan 81° ≈ 10

Also, note that <N is 9° from 90° + 81° + N = 180°
which means that you could also write
tan 9° = x/63
and the answer would be the same.

You can also use the formula to find the hypothenuse and it'll agree with the solution using the Pythagoras' Theorem.

Regards