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

User Rob Wells
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1 Answer

3 votes

Answer:

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 :)

User Dmitry Buzdin
by
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