if a triangle has a hypotenuse of of 10 and an angle of 45 degrees what is the langth of the oppisite side

If a triangle has an hypotenuse, it must be a right triangle.

If a right triangle has one anlge of 45°, the other acute angle must also be 45°.

Therefore, the triangle is an isosceles right triangle.

One way to solve this is to use the Pythagorean Theorem:  a²+ b²  =  c²

c is the hypotenuse   --->   c = 10

Since it's isosceles, a = b, call each one x:     x² + x²  =  10²

                                                                   2x²  =  100

                                                                     x²  =  50

                                                                       x  =  √50  =  √25√2  =  5√2