Question

In the given figure; ∠B = 90°, ∠ADB = 30°, ∠ACB = 45° and AB = 24 m. Find the length of CD.

Answer 1

In right ΔABC,

tan45° = `"AB"/"BC"`

⇒ 1 = `(24)/"BC"`
⇒ BC = 24m.
In right ΔABD,

tan 30° = `"AB"/"BD"`

⇒ `(1)/sqrt(3) = (24)/"BD"`
⇒ BD = `24sqrt(3)"m"`
Now,
CD = BD - BC
= `24sqrt(3) - 24`
= `24(sqrt(3) - 1)"m"`.