2024 · Q51
Consider the following for the next three (03) items that follow: Let ABC be a triangle right-angled at B. Let P be the point on BC such that BP = PC. If AB = 10 cm, ∠BAP = 45° and ∠CAP = θ. What is tanθ equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1/2
- B1/3
- C1/4
- D1/5
Explanation
In right ΔABP, ∠BAP = 45° and AB = 10, so BP = AB·tan45° = 10 cm. Since P is the midpoint of BC, BC = 20 cm. Then tan(∠BAC) = tan(45°+θ) = BC/AB = 2, and (1+tanθ)/(1−tanθ) = 2 gives 3tanθ = 1, i.e. tanθ = 1/3 — option B.