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

Question

asked Mar 2, 2021 95.7k views

2 Answers

Zetafish · Answer 1 · 2021-03-04T05:45:41+0000

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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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