Calculating The Hypotenuse Of A Right-Angled Triangle Using The Pythagorean Theorem

Hypotenuse Chapter 5 (p. 254)

The side opposite the right angle of a right triangle

The hypotenuse is the longest side of a right-angled triangle and is located opposite to the right angle. It is the side that stretches from one of the triangle’s acute angles to the other. The hypotenuse is not always easy to calculate directly, but it can be found using the Pythagorean Theorem.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. It can be expressed as a formula: c² = a² + b², where ‘a’ and ‘b’ are the lengths of the two shorter sides, and ‘c’ is the length of the hypotenuse.

To find the hypotenuse, you need to know the lengths of the two shorter sides of the right-angled triangle. Once you have these values, you can substitute them into the Pythagorean Theorem and solve for the length of the hypotenuse.

For example, if the length of one shorter side is 3 cm and the length of the other shorter side is 4 cm, then the length of the hypotenuse can be calculated as follows:

c² = a² + b²
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25
c = 5

Therefore, the length of the hypotenuse in this triangle is 5 cm.

The hypotenuse is an important concept in trigonometry, as it is used to calculate the sine, cosine, and tangent ratios of an angle in a right-angled triangle. These trigonometric functions allow you to determine the length of a side or the angle of a triangle when given the lengths of the other sides.

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