2021 · Q60
In a triangle ABC, right-angled at B, AB + BC = 10(1 + √3) cm and length of the hypotenuse is 20 cm. What is the value of tanA + tanC ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A4/√3
- B2/√3
- C√3
- D2√3
Explanation
Let AB = x, BC = y; then x + y = 10(1+√3) and x² + y² = 400. Now xy = [(x+y)² − (x²+y²)]/2 = [100(4+2√3) − 400]/2 = 100√3. Since tanA = y/x and tanC = x/y, tanA + tanC = (x²+y²)/xy = 400/(100√3) = 4/√3. This is option (a).