Expert: Sherman D. - 6/18/2005

Question
To: Sherman D.

I need to know the length of the long side and next to longest side of a right triangle. I know the angles formed and the length of one side. I will try to describe the triangle.  Imagine a line starting at a certain point then goes along from the starting point 8 feet horizontally to the right. Then turns 90 degrees straight up. I don't know how long this second line is, but it goes up just far enough then turns back to the starting point and when it reaches the starting point it forms a 30 degree angle.

I would apreciate any help you can give me.
From Francis Choate
repentnow@cox.net

Answer
If you are saying that the 30° forms the hypothenuse and the base, then

a/(sin(A)) = b/(sin(B))
a/(sin(30)) = 8/(sin(60))
a = (8sin(30))/(sin(60))
a = 4/(sqrt(3))/2)
a = (8sqrt(3))/3
a = about 4.6188 feet

c/(sin(90)) = 8/(sin(60))
c = 8/(sin(60))
c = 8/((sqrt(3))/2)
c = (16sqrt(3))/3
c = about 9.2376 feet

a = Vertical Line
b = Horizontal Line
c = Hypothenuse

If you were to use the Pythagorean Thereom, a^2 + b^2 = c^2 you will see that it works out.

If the 30° forms the vertical line and the hypothenuse, then let me know.