Question

In triangle ABC, ∠B = 90° and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.

Answer 1

Consider the figure :

tan A = `(75)/(100) = (3)/(4)`

i.e.`"perpendicular"/"base" = "BC"/"AB" = (3)/(4)`

Therefore if length of base = 4x, length of perpendicular = 3x

Since
BC² + AB² = AC²     ...[ Using Pythagoras Theorem ]

(3x)² + (4x)² = AC²

AC² = 9x² + 16x² = 25x²

∴ Ac = 5x

Now
Ac = 30

5x = 30

x = 6

Therefore
AB = 4x

= 4 x 6

= 24 cm

And
Bc = 3x

= 3 x 6

= 18 cm