Question

If the hypotenuse of a 45-45-90 triangle is 5 sqrt 3 how do I find the two legs?

Answer 1

oke how long is the hypotenuse

Answer 2

All i need is the hypotenuse then i will have the rest for you

Answer 3

the hypotenuse is 5 square root three

Answer 4

ok

Answer 5

125 2√ 2 heres one

Answer 6

its the same for both

Answer 7

I understand its the same but how do I get those two leg answers?

Answer 8

as two sides have same angle (45,45) so these have the same length
so let
hypotenuse = z
1st leg = x
2nd leg = y
from pythagoras theorem
\[z^2 = x^2 + y^2\]
as x = y {same angles}
so \[z^2 = x^2 + x^2\]
\[z^2 = 2x^2\]
putting the values
\[( 5 \sqrt{3} )^2 = 2x^2\]
25(3) = 2x^2
75 = 2x^2
75/2 = x^2
\[\sqrt{37.5} = x \]
So
\[1st leg = \sqrt{37.5} \]
\[2nd leg = \sqrt{37.5} \]

Answer 9

Wow. That's kinda confusing but I think I understand it a little bit better. Thank you very much