Find the height of a right triangle using the Pythagorean theorem
The height of a triangle can be found in different ways, depending on the type of triangle and the information you have or measure. Right triangles, which include an angle of 90 degrees, are the easiest to measure using the Pythagorean theorem (if the lengths of two sides are known) or the formula of the area (if the area and the base are known). The equilateral Triangles, in which all sides are of equal length, and the isosceles triangles, in which three of their sides are of equal length, can be cut in half, creating two right triangles. The oblique triangles, those that do not have the interior angle equal to 90 degrees, are more difficult, and require trigonometry to find their height. Next, we will calculate the height of a right triangle using the Pythagorean theorem
- Scientific calculator
- Conveyor
- Ruler
one
The first thing you have to do to calculate the height of a triangle is to write the Pythagorean theorem, c ^ 2 = a ^ 2 + b ^ 2, where c is the hypotenuse (the diagonal).
two
Reorganize the theorem to solve a ^ 2, so a ^ 2 = c ^ 2 - b ^ 2. We want to find the value of "a" because as we see in the image is the height of the triangle.
3
Connect the two sides of known values cyb, which in our case we will give a value of:
- c = 19
- b = 18
Therefore it remains that [a ^ 2 = 19 ^ 2 - 18 ^ 2]
4
Next we solve the equation and we have to:
a ^ 2 = 361 - 324 = 37
5
To finish and find the real value of the height of the triangle, you have to take the square root of both sides to find the height a ^ 2. [a = 6.1]
- The base can be either side of the triangle.
- The trigonometry method (using sine) can be applied to right triangles as well.
- The three angles of a triangle must add up to 180 degrees.
