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Use the 45º-45º-90º triangle theorem to find the length of the hypotenuse of a right triangle if the legs are 15√2.

Sagot :

mhanifa

Answer:

  • 30 units

Step-by-step explanation:

The ratio of sides in 45º-45º-90º triangle is:

  • a : b : c = 1 : 1 : √2

If both a and b are 15√2, the hypotenuse is:

  • c = 15√2*√2 = 15*2 = 30

Let's consider the given triangle be ∆ABC. First of all we must know the unique property of triangle 45° - 45° - 90°. In this the ratio of sides of the triangle is given by,

[tex]\implies[/tex] a : b : c = 1 : 1 : √2

Now as per your question elaborating it by placing values of sides in our ∆ABC,

Where,

  • c = hypotenuse
  • a & b = two sides

[tex]:\implies\sf{c = 15 \sqrt{2} \times \sqrt{2} }[/tex]

[tex]:\implies\sf{c = 15 \times \sqrt{2} \times \sqrt{2} }[/tex]

[tex]:\implies\sf{c = 15 \times 2}[/tex]

[tex]:\implies\sf{c = 30}[/tex]

  • The length of hypotenuse is 30cm.
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