Question

In ΔABC, if AB/1=AC/2=BC/√3, then m∠C = .....,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 90
(b) 30
(c) 60
(d) 45

Answer 1

Given :

In ∆ABC ,

AB/1 = AC/2 = BC/√3

Let AB/1 = AC/2 = BC/√3 = k

AB = k , AC = 2k , BC = √3k ,

AB² = k² ,

AC² = 4k² ,

BC² = 3k²

Now ,

AB² + BC² = AC²

Therefore ,

<B = 90°

[ By Converse of Phythogarian theorem ]

In ∆ABC,

Sin C = AB/AC

=> SinC = k/2k

=> Sin C = 1/2

=> Sin C = sin 30°

=> C = 30°

Option ( b ) is correct.

••••••••••

Answer 2

Answer:

30°

Step-by-step explanation:

Given :

In ∆ABC ,

AB/1 = AC/2 = BC/√3

Let AB/1 = AC/2 = BC/√3 = k

AB = k , AC = 2k , BC = √3k ,

AB² = k² ,

AC² = 4k² ,

BC² = 3k²

Now ,

AB² + BC² = AC²

Therefore ,

<B = 90°

[ By Converse of Phythogarian theorem ]

In ∆ABC,

Sin C = AB/AC

=> SinC = k/2k

=> Sin C = 1/2

=> Sin C = sin 30°

=> C = 30°

Hopefully it's helpful to you!!!