Will mark brainliest if right
in right △abc, the altitude

ch

to the hypotenuse

ab

intersects angle bisector

al

in point d. find the sides of △abc if ad = 8 cm and dh = 4 cm.

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

In ΔAHD, the side opposite angle DAH is DH, and the hypotenuse is AD, so we have ...

  sin(∠DAH) = DH/AD = 4/8

  ∠DAH = arcsin(4/8) = 30°

That makes ΔAHD a 30°-60°-90° triangle, so the side lengths have the ratios 1 : √3 : 2.

∠CAB = 2·30° = 60°, so ΔABC is also a 30°-60°-90° triangle having the same ratios of side lengths.

In short, ...

  AH = √3·DH = 4√3

  AC = 2·AH = 8√3

  AB = 2·AC = 16√3

  BC = √3·AC = 8·(√3)² = 24

what i would say the best answer is a. 40.5

jml angle lkj & angle mj = lm