Question

Find the length of the legs of a 45°- 45°-90° triangle with a hypotenuse of 4.

Answer 1

note that you have 45-45-90
this only implies that the legs are having the same length.
using pythagorean theorem you'll have:
\[c^2 = a^2 + b^2\]
and since a is equal to b then
\[c^2 = a^2 + a^2\]
\[c^2 = 2a^2\]
c=4
substituting the value of c:
\[4^2 = 2a^2\]
\[a^2 = \frac{ 16 }{ 2 }\]
\[a^2 = 8\]
\[a = \sqrt{8}\]
\[a = \sqrt{4\times2}\]
\[a = 2\sqrt{2}\]

Answer 2

Thank you so much for explaining it completely !