Question

Help I’ll give you Brainleiest

Answer 1

Answer:

6 cm

Step-by-step explanation:

I don't know may I use the trigonometry functions, therefor I'm going to use Pythagorean theorem and property of 30°-60°-90° triangle.

m∠ACB = 120° ⇒ m∠ACD = 60° ⇒ m∠DAC = 30°

DC is opposite to 30° angle ⇒ AC = CB = 8 cm

From ΔADC: AD² = 64 - 16 = 48 ; AD = 4√3 cm

ΔACB is isosceles ⇒ m∠CAB = m∠CBA = 30°

m∠DAH = m∠DAC + m∠CBA = 2(30°) = 60° ⇒ m∠ADH = 30° ⇒ AH = 4√3 ÷ 2 = 2√3 cm

From ΔADH: DH = $\sqrt{48-12}$ = √36 = 6 cm