In △DCE, DC = CE = 6, m∠E = 53º. Find DE.

So I tried to use tan or cot but there isn't a 90 degree angle C is 74 i somehow got 7.22 but i can't really explain how.

3 answers

since the triangle is isosceles,
m∠D = m∠E = 53º
so, m∠C = 74º

so, (DE/2)/6 = sin(74/2)º
DE/12 = sin37º
DE = 12 sin37º = 7.22

or, using the law of sines,
DE/sin74º = 6/sin53º
DE = 7.22

or, using the law of cosines,
DE^2 = 6^2+6^2 - 2*6*6 cos74º
DE = 7.22

As you can see, the key to this was getting angle C

Thank you!

Thanks so much