Instruction
1
You can find out the size of the third parties, knowing the lengths of two other sides of the triangle. This can be done by using the Pythagorean theorem, which States that the square of the hypotenuse of a rectangular triangle is equal to the sum of the squares of the other two sides. (a2 = b2+ c2). Hence, we can Express the lengths of all sides of a rectangular triangle:
b2 = a2 - c2;
c2 = a2 - b2
For example, a rectangular triangle are known, the length of the hypotenuse a (18 cm) and one of the legs, for example c (14 cm). To find the length of the other leg, you want to make 2 algebraic operations:
S2 = 182 - 142 = 324 - 196 = 128 cm
c = √128 cm
Answer: the length of the second leg is √128 cm or approximately 11.3 cm
2
You can resort to another method if you know the length of the hypotenuse and the magnitude of one of the acute angles of the rectangular triangle. Let the length of the hypotenuse equal to c, one of the acute angles equal to α. In this case, find the 2 other side of rectangular triangle will be using the following formulas:
a = s*sinα;
b = s*cosα.
Example: the length of the hypotenuse is 15 cm, one of the acute angles is 30 degrees. To find the lengths of the other two sides you need to perform 2 steps:
a = 15*sin30 = 15*0.5 = 7.5 cm
b = 15*cos30 = (15*√3)/2 = 13 cm (approx)
3
The most trivial way to find the length of sides of a rectangular triangle is to Express it from the perimeter of this shape:
P = a + b + c, where P is the perimeter of a rectangular triangle. From this expression it is easy to Express the length of any of sides of a rectangular triangle.