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ABCD is a trapezium such that AB and CD are parallel and AB ⟂ CD. If ∠ADB = θ, BC = p and CD = q, then AB is equal to:

1. (p² + q²) sinθ / (p cosθ + q sinθ)
2. (p² + q² cosθ) / (p cosθ + q sinθ)
3. (p² + q²) / (p² cosθ + q² sinθ)
4. (p² + q²) sinθ / (p cosθ + q sinθ)²

Correct answer: (p² + q²) sinθ / (p cosθ + q sinθ)

Solution

Using the right triangle relations in the trapezium, AB = (p^2 + q^2) sin(theta) / (p cos(theta) + q sin(theta)). The denominator appears to the first power, not squared.

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