Given: ΔАВС, m∠ACB = 90° CD ⊥ AB, m∠ACD = 30° AD= 6 cm. Find: BD

PART 1
Use ratio of sin to find AC
sin of an angle = side in front of the angle / hypotenuse

Look at ΔACD
cos of an angle = side in front of the angle / hypotenuse
cos 30° = AD/AC
1/2 = 6/AC
AC/2 = 6
AC = 6 × 2
AC = 12
The length of AC is 12 cm

PART 2
Find the measure of ∠CAD
∠CAD + ∠ACD + ∠ADC = 180°
∠CAD + 30° + 90° = 180°
∠CAD + 120° = 180°
∠CAD = 180° - 120°
∠CAD = 60°

∠CAB = ∠CAD
∠CAB = 60°

PART 3
Use ratio of cos to find AB
cos of an angle = side adjacent to the angle / hypotenuse

Look at ΔABC
cos of an angle = side adjacent to the angle / hypotenuse
cos ∠CAB = AC/AB
cos 60° = 12/AB
1/2 = 12/AB
AB/2 = 12
AB = 12 × 2
AB = 24
The length of AB is 24 cm

PART 4
Find BD
BD = AB - AD
BD = 24 - 6
BD = 18
The length of BD is 18 cm