How to find a corner in a rectangular triangle

How to find a corner in a rectangular triangle

Already from the name of a ""rectangular"" triangle it becomes clear that one corner in it makes 90 degrees. Other corners can be found, having remembered simple theorems and properties of triangles.

It is required to you

  • Table of sine and cosines, Bradis's table


1. Let's designate triangle corners by the letters A, B and C as it is shown in the drawing. The corner of BAC is equal 90º, we will designate two other corners by letters α and β. We will designate legs of a triangle by letters an and b, and a hypotenuse a letter with.

2. Then sinα = b/c, and cosα = a/c. Similarly for the second acute angle of a triangle: sinβ = a/c, and cosβ = b/c. Depending on what parties are known to us, we calculate sine or cosines of corners and we watch according to Bradis's table value α and β.

3. Having found one of corners, it is possible to remember that the sum of internal corners of a triangle is equal 180º. Means, the sum α and β is equal 180º - 90º = 90º.Тогда, having calculated value for α according to tables, we can β use the following formula for location: β = 90º - α

4. If one of the parties of a triangle is unknown, then we apply Pythagorean theorem: a²+b²=c². Let's bring out of it expression for the unknown party through two others and we will substitute in a formula for finding of a sine or a cosine of one of corners.

Author: «MirrorInfo» Dream Team