How to Find the Height of an Oblique Triangle With Area
The height of a triangle can be found in different ways, depending on the type of triangle and the information that is measured. Rectangular triangles, which include an angle of 90 degrees, are easiest to measure using the Pythagorean theorem (if the lengths of both sides are known) or the area formula (if the area and base are known). Equilateral triangles, where all sides are of equal length, and isosceles triangles where three sides are equal in length, can be cut in half, creating two triangles. But oblique triangles, whose inside angle equals 90 degrees, are harder and require trigonometry to find out their height. Then, you calculate the height of an oblique triangle using the area formula.
ttttFirst, draw the triangle and appoint the sides and known values.
- A, B and C are the angles.
- a, b, c are the sides
- h is the height
In this example, A = 60 degrees and b = 5.
Enter the area formula:
- A = 1/2 bh (A = area, b = base, h = height)
All values are not required, but the formula helps to keep everything correctly oriented.
Look for the side adjacent to the base. [Side b = 5]
Find the angle adjacent to the base and the side in step 3. If you do not know, a protractor will help you when measuring the angle. [Angle A = 60]
Enter the height formula, which is the side adjacent to the base, multiplied by the sine of the angle adjacent to the side. [h = 5sin60]
Perform calculations to find the height. [h = 5 x 0.87 = 4,33]
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- The base may be any side of the triangle.
- The method of trigonometry (using sine) can also be applied to triangles.
- The three angles of a triangle must add up to 180 degrees.