How to Calculate the Altitude of a Triangle
You can find the altitude of a triangle in one of two ways. The first requires you to know the length of the base and the area of the triangle. The second requires you to know the measurement of at least one of the triangle's interior angles, located opposite from the altitude, and the length of the hypotenuse of the right triangle created by drawing the altitude. Either of these methods enables you to find the triangle altitude in a relatively straightforward manner.
Other People Are Reading
Instructions
-
Calculating Altitude From Base and Area
-
1
Obtain the value of the triangle area, from information given in the problem that you are solving.
-
2
Measure the length of the base, if it is drawn to scale, or obtain the base length from the problem that you are solving.
-
-
3
Plug the values of the area and the base into the triangle area formula: area = b*h/2, in which "b" equals the base and "h" equals the triangle altitude. Solve for the value of h. If the area is equal to 10 square meters and the base is equal to 2 meters, for instance, the height must equal 10 meters.
Using Trigonmetry to find Triangle Altitude
-
4
Draw a line from the highest point of the triangle to the base of the triangle, forming two right triangles within the triangle.
-
5
Set up a trigonometric identity. You should use the value of the angle opposite to the line that you drew between the vertex and base, as well as the length of the hypotenuse of the right triangle that you calculated. If, for instance, the value of that angle is 60 degrees and the length of the hypotenuse is 6, you can use the trigonometric identity, sin 60 = (altitude)/6.
-
6
Solve for the altitude. In the example, the altitude is equal to 6*sin(60)=5.196.
-
1
