Solution of the right-angled triangle
The angle O is bound by the lines OA and OB. If a line is drawn from anywhere on line OA, perpendicular up to the line OB from point M to point P then a right-angled triangle is created.
The ratio MP/OP is called the sine of angle AOB.
The ratio OM/OP is called the cosine of angle AOB.
The ratio MP/OM is called the tangent of angle AOB.
The abbreviation sin is usually used for sine.
In any right angled triangle,
sine of the angle = side opposite the angle / hypotenuse
Example
Note that all the angles in a triangle add up to 180 degrees.
The abbreviation cos is usually used for cosine.
In any right angled triangle,
cosine of the angle = side adjacent to the angle / hypotenuse
Example
Note that all the angles in a triangle add up to 180 degrees.
The abbreviation tan is usually used for tangent.
In any right angled triangle,
tangent of the angle = side opposite the angle / side adjacent to the angle
Example 1
Note that all the angles in a triangle add up to 180 degrees.
Example 2
Solution of the right-angled triangle
| Known Data | |||
| a & b |  |  |  |
| a & c |  |  |  |
| b & c |  |  | |
| a & B |  |  | |
| a & C |  |  | |
| b & B |  |  | |
| b & C |  |  | |
| c & B |  |  | |
| c & C |  |  | |
The above diagram shows the relationship between sin, cos and tan.
If the circle has a radius other than 1 then the sin, cos or tan are multiplied by the radius.
Example
Problem part
Solution
