RIGHT TRIANGLE

The right triangle is a triangle where is one of its interior angles is a right angle (90 degrees).

Right triangles figure prominently in various branches of mathematics. For example, trigonometry concerns itself almost exclusively with the properties of right triangles, and the famous theorem by Pythagoras defines the relationship between the three sides of a right triangle:
a^2 + b^2 = h^2
where h is the length of the hypotenuse
a, b are the lengths of the other two sides

Attributes
Hypotenuse : The side opposite the right angle. This will always be the longest side of a right triangle.
Sides : The two sides that are not the hypotenuse. They are the two sides making up the right angle itself.

Properties
• A right triangle can also be isosceles if the two sides that include the right angle are equal in length (AB and BC in the figure above)
• A right triangle can never be equilateral, since the hypotenuse (the side opposite the right angle) is always longer than the other two sides.

Things to Ponder
1. Can a right triangle also be isosceles?
Yes, if its sides have the same length. In the diagram above, try to create such a triangle

2. Can a right triangle also be a scalene triangle?
Yes, if the two sides have different length. The hypotenuse is always the longest side, so it must be a different length to the sides

3. One angle of a right triangle is 41°. What are the other two?
49° and 90°. The interior angles of any triangle always add up to 180°

4. What is the area of a right triangle with sides of length 12 and 15cm?
Somewhere between 89 and 94 square cm

5. A right triangle has a hypotenuse 10 meters long, and one leg 6 meters long. What is the length of the other leg?
Somewhere between 7.1 and 8.9 meters