Question

In the adjoining figure, CD = 48 cm, tan ф = `5/12` and tan = `3/4`. Find the length of AB and BC.

Answer 1

Using the given tangents:

Let BC = 4k and AB = 3k   ...`(because tan ф = "AB"/"BC" = 3/4)`

From point D the adjacent to angle θ is DB = BC + CD = 4k + 48. 

So, `tan θ = "AB"/("BC" + 48)`

= `(3k)/(4k + 48)` 

= `5/12`

Solve: 12 × 3k = 5(4k + 48) 

36k = 20k + 240

16k = 240 

⇒ k = 15

Therefore, BC = 4k = 60 cm and AB = 3k = 45 cm.