Advertisements
Advertisements
Question
In the given figure; ∠B = 90°, ∠ADB = 30°, ∠ACB = 45° and AB = 24 m. Find the length of CD.
Advertisements
Solution
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"`.
APPEARS IN
RELATED QUESTIONS
If 2 sin x° − 1 = 0 and x° is an acute angle; find:
- sin x°
- x°
- cos x° and tan x°.
Solve the following equation for A, if 2cos2A = 1
Solve the following equation for A, if `sqrt3` cot 2 A = 1
If sin 3A = 1 and 0 < A < 90°, find cos 2A
Find the value of 'A', if cot 3A = 1
Solve for 'θ': `sin θ/(3)` = 1
If `sqrt(2) = 1.414 and sqrt(3) = 1.732`, find the value of the following correct to two decimal places tan60°
If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`
Evaluate the following: cot20° cot40° cot45° cot50° cot70°
If cos3θ = sin(θ - 34°), find the value of θ if 3θ is an acute angle.
