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
