Question

Calculate the length of AC if BD=30cm,∆ABC=30° and ∆ADC=45°​

Answer 1

Step-by-step explanation:

Let length of AB=x cm.

In right angled triangle ABD , AB/BD=tan 45°.

or. x/BD = 1 => BD=x cm.

BC= BD-CD = (x-30) cm.

In right angled triangle ABC , AB/BC= tan60°

or. x/(x-30) = √3.

or. √3.x -30√3 = x.

or. x(√3–1) = 30√3.

or. x= 30.√3/(√3–1) = 30√3×(√3+1)/(√3–1).(√3+1).

or. x =15√3(√3+1) = 15(3+√3) cm = 70.98 cm.

Thus , length of AB= x = 70.98 cm.

and length of BC= (x-30) = 40.98 cm. Answer.