2024 · Q52
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. If ∠ACP = γ, then what is tanγ equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1/2
- B1/3
- C2/3
- D1
Explanation
Since P lies on BC, ∠ACP is the same angle as ∠ACB of the whole triangle. In right ΔABC, tan(∠ACB) = opposite/adjacent = AB/BC. With AB = 10 and BC = 20 (P bisects BC and BP = 10 from Q51), tanγ = 10/20 = 1/2 — option A.