High School

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3. Find the lengths of sides marked with letter in each of the following right-angled triangles.

* **Triangle 1:**
* One side: 8cm
* Another side: 15cm
* Find the hypotenuse (P)
* P = √(15² + 8²) = √(289) = 17cm

* **Triangle 2:**
* One side: 3cm
* Another side: 5cm
* Find the hypotenuse (C)
* C = √(3² + 5²) = √(34)cm

Answer :

To find the lengths of the hypotenuses in the given right-angled triangles, we use the Pythagorean Theorem. This theorem 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.

Let's examine each triangle separately:

  1. Triangle 1:

    • Given sides: 15 cm and 8 cm.
    • We need to find the hypotenuse (denoted as [tex]P[/tex]).

    Using the Pythagorean Theorem:
    [tex]P = \sqrt{15^2 + 8^2}[/tex]
    Calculating inside the square root:
    [tex]15^2 = 225[/tex]
    [tex]8^2 = 64[/tex]
    Therefore:
    [tex]P = \sqrt{225 + 64} = \sqrt{289}[/tex]
    [tex]P = 17[/tex] cm

  2. Triangle 2:

    • Given sides: 3 cm and 5 cm.
    • We need to find the hypotenuse (denoted as [tex]C[/tex]).

    Again, using the Pythagorean Theorem:
    [tex]C = \sqrt{3^2 + 5^2}[/tex]
    Calculating inside the square root:
    [tex]3^2 = 9[/tex]
    [tex]5^2 = 25[/tex]
    Therefore:
    [tex]C = \sqrt{9 + 25} = \sqrt{34}[/tex]
    [tex]C \approx 5.83[/tex] cm

These calculations allow us to determine the hypotenuse for each triangle based on the Pythagorean Theorem, a fundamental principle used in geometry to find missing side lengths in right-angled triangles.

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