The height of a triangle can be found in different ways, depending on the type of triangle and the information that is held or measured. **Right Triangles, which include a 90 degree angle, are the easiest to measure using the Pythagorean Theorem **(if the lengths of two sides are known) or the formula for the area (if the area and the base are known).**Equilateral Triangles**, in which all the sides are of equal length, and isosceles triangles, in which three of their sides are of equal length, can be cut in half, creating two right triangles. Oblique triangles, those that do not have an interior angle equal to 90 degrees, are more difficult, and require trigonometry to find their height.** the height of a right triangle** using the Pythagorean theorem

Steps to follow:

1

The first thing you have to do to calculate the height of a triangle is to write the **Pythagoras theorem**, c ^ 2 = a ^ 2 + b ^ 2, where c is the hypotenuse (the diagonal).

2

Rearrange the theorem to solve a ^ 2, so that a ^ 2 = c ^ 2 – b ^ 2. We want to find the value of “a” since, as we see in the image, it is the height of the triangle.

3

Connect the two sides of known values c and b, which in our case we are going to give a value of:

Therefore it remains that [a ^ 2 = 19 ^ 2 – 18 ^ 2]

4

Next we solve the equation and we have:

a ^ 2 = 361 – 324 = 37

5

To finish and find the true 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]

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Advice

- 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.