Right Triangles

A Triangle has three sides and three angles. A Right Triangle has an angle that is 90 degrees.

right triangle with hypotenuse h, angle theta, opposite side o and adjacent side a

If you haven’t studied angles yet, at 9 O’clock, the angle between the two clock hands is 90°. In the above graphic, the right angle is between the blue and purple sides. The angle theta is between the yellow side and the blue side; theta is a Greek letter that is like a zero with a small horizontal line segment in the middle. \theta

The side of a triangle opposite to the right angle is called the Hypotenuse.

If we select one of the angles of the triangle that is not the right angle as our frame of reference then we can define a side of the triangle is being opposite in a side of the triangle is being adjacent.

Appendix A

There are two right triangles that we find to be especially important.

A triangle with sides 3,4,5 helps to illustrate the Pythagorean theorem because we can easily see the following:

  • 9+16=25
  • 3*3=9
  • 4*4=16
  • 5*5=25

Another triangle is important: 1,1.732,2

This triangle is interesting because its angles, in degrees, are 30, 60, 90.

Appendix B

Right triangles are so important that our webpage about Right Triangles was made before we made a page about Triangles.

Right triangles are present in the calculations for Component Forces in Physics. A sled is sliding down an inclined plane and gravity is pulling straught down but we want to ask two questions:

  1. How much is gravity pulling in the direction that the sled is sliding?
  2. How much is gravity pulling into the inclined plane?

Other calculation to answer these questions makes use of a right triangle.