Expert: Ahmed Salami - 6/19/2004

Question
I am building a ramp for a wheelchair-bound relative. I took a 5 foot board, propped it against the doorway, and now I want to put some supports underneath the ramp, but I don't know at what angle I should cut them. I don't have a protractor, but even if I did, I want to know if there is a mathematical way in which to figure out the angle. I know the length of all three sides of the "triangle" and I know that one anle of the triangle is 90 degrees. Is there a way to figure out the other angles?

Answer
Hi Johann,
Sorry about the delay.
There is always a trigonometric way out of problems like this one.
since one of the angles is 90 degrees, this triangle is a right angled triangle.
Label the sides as a,b,c and the angles as A,B,C . The angle of a side is the angle with which it does not have any contact.
we now use the formula,
a/sinA = b/sinB = c/sinC
we know one angle to be 90 degrees and its side is the longest,c. But sin 90 = 1
if we know a and b and require to find A and B, we just say
a/sinA = c
and b/sinB = c
You will definitely get it.
I hope i have helped.
regards.