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

CD = 6 units

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