Question

There is a right isosceles triangle. The hypotenuse is 31. Find the value of the two missing legs. Round the answer to the nearest 100th.

if possible, I would like to learn the formula for future reference.

Answer 1

we know that
A right isosceles triangle has two equal sides and two equal angles
so
has two angles equals to 45°

methodology 1 to solve the problem
Let
x--------> length of the leg of triangle
sin 45°=opposite side/hypotenuse
sin 45°=√2/2
opposite side=hypotenuse*sin 45°------> 31*√2/2---> 21.92 units


methodology 2 to solve the problem
c²=a²+b²
c=hypotenuse------> 31 units
a=leg 1
b=leg 2
a=b
so
c²=2a²------> a²=c²/2------> a²=(31)²/2
a=√[(31)²/2]------> a=31/√2-----> 31√2/2------> 21.92 units