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Kituo cha Kujifunza / Jiometri

The Pythagorean theorem

How a² + b² = c² finds a missing side of any right triangle, plus the triples worth remembering.

Dakika 1 za kusomaImesasishwa 18 Oktoba 2026Na Sumzo teamImekaguliwa na Sumzo team

In a right triangle, the side opposite the right angle is the hypotenuse cc — always the longest side. The other two sides are the legs aa and bb.

a2+b2=c2a^2 + b^2 = c^2

Mfano uliotatuliwa

Find the hypotenuse

A right triangle has legs 3 and 4. How long is the hypotenuse?

Onyesha hatua za suluhisho
  1. Square and add the legs.
    c2=32+42=25c^2 = 3^2 + 4^2 = 25
  2. Take the square root.
    c=25=5c = \sqrt{25} = 5

Jibu: 5

Imekaguliwa na injini ya hisabati ya Sumzo

Finding a leg

Rearrange to b2=c2−a2b^2 = c^2 - a^2: subtract instead of adding.

Mfano uliotatuliwa

Find a missing leg

A right triangle has hypotenuse 13 and one leg 5. Find the other leg.

Onyesha hatua za suluhisho
  1. Subtract the squares.
    b2=132−52=144b^2 = 13^2 - 5^2 = 144
  2. Take the square root.
    b=12b = 12

Jibu: 12

Imekaguliwa na injini ya hisabati ya Sumzo

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