Question

In triangle ABC, the measure of angle BCA is 90, segment AC is 12 units, and segment BC is 9 units. If D is a point on hypotenuse AB, such that segment AD is 5 units, what is the length of segment CD? Express your answer is simplest radical form.

Answer 1

Answer:

CD = 6 units

Step-by-step explanation:

In triangle ABC , AB is the hypotenuse then    AB =√(BC)² + (AC)²  = √(12)² + (9)²   =  15

AB = 15

sin ∠ABC  12/15   = 0,8   Then   arcsin (0.8)  =  53,1°

∠ABC  = 53,1°      and   ∠BAC  =  36,9°

Now the hypotenuse is 15 units and we need to find the lenght of segment

CD. If we divide the hypotenuse in three equal segment (of lenght 5 each) we at the same time are dividing the ∠ACB ( 90°),  in three equals angles of

30°.

If we now apply sin law

sin 30°/ 5    = sin 36,9°/CD

Then    CD  = 5 * sin 36.9° / sin 30°   ⇒  CD =[ 5* (9/15) ] / 1/2

CD = 6 units