Question

In this 45-46-90 triangle , I have been given the length of a leg . How do I find the length of the hypotenuse

Answer 1

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Sum of the interior angles of any triangle equal 180° .

Thus ;

The angle which facing to the side 4 is 45°.

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Hint :

In a right triangle, the side facing the 45° angle is √2 / 2 times the hypothenuse .

Thus ;

`( √(2) )/(2) x = 4 \\`

Multiply sides by 2

`2 * ( √(2) )/(2) x = 2 * 4 \\`

`√(2) x = 8 \\`

Divide sides by √2

`( √(2)x )/( √(2) ) = (8)/( √(2) ) \\`

`x = (4 * 2)/( √(2) ) \\`

`x = (4 * √(2) * √(2) )/( √(2) ) \\`

`x = 4 √(2) \\`

`x = hypothenuse = 4 √(2)`

Done...

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Answer 2

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