Question

If A(1, 2) B(-3, 2) and C(3, -2) be the vertices of a ∆ABC show that tanA=2

Answer 1

Proof:

The vertices of the triangle ΔABC are A (1, 2), B (- 3, 2) and C (3, - 2). The sides of the triangle are AB, BC, CA and we have to find the tangent ratio of the angle A.

The slope of the line AB is

m₁ = (2 - 2) / (- 3 - 1)

= 0 and

that of the line CA is

m₂ = (2 + 2) / (1 - 3)

= - 2

Then the angle A is determined from

tanA = (m₁ - m₂) / (1 + m₁m₂)

= (0 + 2) / (1 + 0)

= 2

Hence tanA = 2

This completes the proof.