Question
Solve: please include statement and reason
Given: ΔАВС, m∠ACB = 90°
CD ⊥ AB, m∠ACD = 30°
AD = 6 cm.
Find: BD
Given: ΔАВС, m∠ACB = 90°
CD ⊥ AB, m∠ACD = 30°
AD = 6 cm.
Find: BD
Answers
Damon
m∠ACD = 30°
sin 30 = 1/2 = AD / AC = 6 /AC
so AC = 12
tan 60 = CB/12
so CB = 12 tan 60
sin 60 = BD/CB = BD/ (12 tan 60)
BD = 12 sin 60 tan 60 = 12 (.5 sqrt 3)(sqrt 3) = 6*3 = 18
sin 30 = 1/2 = AD / AC = 6 /AC
so AC = 12
tan 60 = CB/12
so CB = 12 tan 60
sin 60 = BD/CB = BD/ (12 tan 60)
BD = 12 sin 60 tan 60 = 12 (.5 sqrt 3)(sqrt 3) = 6*3 = 18
Reiny
You have a 30-60-90° triangle
You should know the ratio of sides are : 1:√3:2
so CD/6 = √3:1
CD = 6√3
You should know the ratio of sides are : 1:√3:2
so CD/6 = √3:1
CD = 6√3