Find m<ABD to the nearest degree

Question

Right triangle ABC has a right angle at B. Segment BD is an altitude to the hypotenuse. DC=5 and AD=16. Find m<ABD to the nearest degree

Answer 1

An altitude to the hypotenuse is the mean proportional between the two segments

 

16 : BD :: BD : 5

BD² = 80

BD = 4√5

 

Use tangent to determine m∠ABD