# Triangle Problem

• Mar 19th 2012, 04:05 PM
Proclivitas
Triangle Problem
The tangent of 64 degrees is approx 2. In a right triangle the length of the side opposite a 54 degree angle is approx ? times the length of the side adjacent.

Please solve, I have no idea how to do this one.
• Mar 19th 2012, 04:12 PM
Xeritas
Re: Triangle Problem
Which adjacent side, the hypotenuse, or the other?
• Mar 19th 2012, 04:13 PM
Proclivitas
Re: Triangle Problem
I was hoping you knew.
• Mar 19th 2012, 04:18 PM
Xeritas
Re: Triangle Problem
Well you'd have two different answers, but I'm assuming that it is not referring to the hypotenuse. I believe that the sides should be proportional to the degree of the angles, but could be wrong. This basically means that you need to find the other angle, then divide the 54 degrees by the other angle to get your answer.

Knowing that there are 180 degrees in a triangle, and two of the angles are 90 and 54 degrees...

180-90-54=36

Since you want to know how many times the side opposite the 54 degree angle is larger(or smaller) than the adjacent side, you will divide 54 by 36 degrees. You should end up with 1.5.
• Mar 19th 2012, 04:55 PM
bjhopper
Re: Triangle Problem
an acute angle in a right triangle has an opposite leg (the away leg) and an adjacent leg (the near leg). A 54deg angle in such a triangle has atangent = opp leg/near leg =1.38