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 ;

$\frac{ \sqrt{2} }{2} x = 4$

Multiply sides by 2

$2 \times \frac{ \sqrt{2} }{2} x = 2 \times 4$

$\sqrt{2} x = 8$

Divide sides by √2

$\frac{ \sqrt{2}x }{ \sqrt{2} } = \frac{8}{ \sqrt{2} }$

$x = \frac{4 \times 2}{ \sqrt{2} }$

$x = \frac{4 \times \sqrt{2} \times \sqrt{2} }{ \sqrt{2} }$

$x = 4 \sqrt{2}$

$x = hypothenuse = 4 \sqrt{2}$

Done...

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Answer 2

Answer:

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