Question

In triangle ABC; ∠ABC = 90°, ∠CAB = x°, tan x° = `(3)/(4)` and BC = 15 cm. Find the measures of AB and AC.

Answer 1

Consider the figure:

tan x° = `(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

AC² = 25x²

AC = `sqrt(25x^2)`

∴ AC = 5x 

Now 
BC = 15

3x = 15

x = `15/3`

x = 5

Therefore

AB = 4x

= 4 × 5

= 20 cm

And
AC = 5x

= 5 × 5

= 25 cm