JEE Main2013MathematicsHeights and DistancesActual
A B C D is a trapezium such that A B and C D are parallel and B C ⊥ C D . If ∠ A D B = θ , B C = p and C D = q , then A B is equal to
Options
- Ap 2 + q 2 p 2 cos θ + q 2 sin θ
- Bp 2 + q 2 sin θ p cos θ + q sin θ 2
- Cp 2 + q 2 sin θ p cos θ + q sin θ
- Dp 2 + q 2 cos θ p cos θ + q sin θ
Correct answer
C. p 2 + q 2 sin θ p cos θ + q sin θ
Step-by-step solution
Let ∠ B D C = α , then tan α = B C C D = p q A E = B C = p tan α + θ = A E E D ⇒ E D = p tan α + θ = p 1 - tan α tan θ tan α + tan θ = p 1 - p q tan θ p q + tan θ Now, A B = q - E D = q - p q - p tan θ p q + q tan θ = p q + q 2 tan θ - p q + p 2 tan θ p + q tan θ = p 2 + q 2 tan θ p + q tan θ = p 2 + q 2 sin θ p cos θ + q sin θ