Answer:
Explanation:
This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.
There is a Pythagorean triple that goes along with a 30-60-90 triangle:
( x , x√3 , 2x )
where each value there is the side length across from the
30 , 60 , 90 degree angles.
We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,
2x = 2√13
and we need to solve for x. Divide both sides by 2 to get that
x = √13
Now we can solve the triangle.
The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.
The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.
And we're done!