Understanding the Formula and Working Out Examples of a Right Triangle

The triangle is a shape that has three sides and three angles. A right triangle is a triangle that has one angle that is 90 degrees. Knowing the formula for the height of a right triangle is important for those who need to calculate the area of the triangle and the hypotenuse.

Formula for Calculating the Height of a Right Triangle

The formula for calculating the height of a right triangle is a2 + b2 = c2, where a and b are the two shorter sides of the triangle and c is the hypotenuse. To find the height of the triangle, you will need to use the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Examples of Right Triangle Height Calculation

Let’s look at a few examples of how to calculate the height of a right triangle. Take the right triangle below with a=3, b=4 and c=5.

Using the Pythagorean Theorem, the height of the triangle can be calculated by solving for h in the equation h2 = 32 + 42. The height of the triangle would be h = √25 = 5.

Application of Right Triangle Height Calculation to Real-Life Situations

The height of a right triangle can be used to calculate the area of the triangle. The area of a triangle is equal to ½ of the base multiplied by the height. For example, if a right triangle has a base of 8 and a height of 10, the area of the triangle would be 8 x 10 = 80. Knowing the height of a right triangle can also help determine the length of the hypotenuse.

Conclusion

The formula for calculating the height of a right triangle is a2 + b2 = c2, where a and b are the two shorter sides of the triangle and c is the hypotenuse. Examples of how to calculate the height of a right triangle include using the Pythagorean Theorem. The height of a right triangle can also be used to calculate the area of the triangle and the length of the hypotenuse.