How to use Pythagoras theorem to show that an angle is 90

Answer 1

To show that an angle is 90 degrees using Pythagoras theorem, you need to use either a right-angled triangle or prove that a triangle is a right-angled triangle.

Here's how you can use Pythagoras theorem to show that an angle is 90 degrees in a right-angled triangle:

1. Identify a right-angled triangle where one of the angles is unknown.

2. Use Pythagoras theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

3. If, after calculating the squares of the sides and applying Pythagoras theorem, you find that the equation holds true, then the triangle is a right-angled triangle and the unknown angle is 90 degrees.

For example, if you have a right-angled triangle with sides of length 3, 4, and 5 units, you can use Pythagoras theorem to show that the angle opposite the side of length 5 is 90 degrees. This is because 3^2 + 4^2 = 9 + 16 = 25, which is equal to 5^2.

Therefore, the angle opposite the side of length 5 in this triangle is 90 degrees.