For any right triangles we can apply the Pythagorean theorem which is given below:
a2 + b2 = c2, where c is the opposite side to the right angle called hypotenus and the other two sides are called catheti.
the Pythagorean theorem can be rewritten as:
a = (c2 - b2)1/2
b = (c2 - a2)1/2
c = (a2 + b2)1/2
Example 1 (When two sides are known)
When two of the 3 sides are known in a right triangle the third side can always be determined by using one of the three equations above.
a = 3
b = 4
the hypotenus c can then be determined as followed:
c = (a2 + b2)1/2=(32 + 42)1/2=251/2= 5
Note: If the length of c is twice the length of a, then the angle A and B must be 30o and 60o respectively.
Example 2 (When one angle and one side are known)
By using trigonometric functions, we can easily determine the lengths of any sides when one angle (beside the right angle) and one side are known.
A = 30o
c = 6
to determine the length of a we can use the following equation:
sin (A) = a/c which can be rewritten as a = sin (A) x c = sin (30o) x 6 = 3
to determine the length of b we can use the following equation:
cos (A) = b/c which can be rewritten as b = cos (A) x c = cos (30o) x 6 = 5.196
other trigonometric functions available are:
tan (A) = a/b
cot (A) = b/a