Question

Determine the number of possible triangles, ABC, that can be formed given angle A = 30°, a = 4, and b = 6.

Answer 1

Explanation:

Alright, lets get started.

using Sine Law,

`(sinA)/(a)=(sinB)/(b)`

`(sin30)/(4)=(sinB)/(6)`

`sinB=0.75`

`angle B = 48.6`

Another angle will be

`angle B' = 180-48.6 = 131.4`

considering angle B, angle C =
`180 - (48.6+30)=101.4`

considering angle B', angle C' =
`180-(131.4+30)=18.6`

`(sinA)/(a)=(sinC)/(c)`

`(sin30)/(4)=(sin101.4)/(c)`

`c = 7.84`

Similarly, finding c'

`(sinA)/(a)=(sinC')/(c')`

`(sin30)/(4)=(sin18.6)/(c')`

`c'=2.55`

Hence two triangles are possible with below details: : Answer

A = 30, B = 48.6, C = 101.4, c = 7.84

A = 30, B' = 131.4, C' = 18.6, c' = 2.55

Hope it will help :)