Question

Hey guys 25 points!! to help me out

In △DEF, DF = 16 and m∠F=45. Find the length of a leg. Leave your answer in simplest radical form.

Answer 1

we have here an isosceles right triangle because there is a right angle and a 45 degree angle, and the m<D=45 as well
the hypotenuse is 16
we use the formula c^2=a^2+b^2
now we have a=b because the triangle is isosceles
c^2=2(a^2)
256=2(a^2)
256/2=a^2
128=a^2
a= 11.31 and b=11.31

Answer 2

the answer is 8 root 2