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Question: If A = 30<sup>0</sup>, a = 7, b= 8 in ∆ABC, then B has...

If A = 300, a = 7, b= 8 in ∆ABC, then B has

A

One solution

B

Two solutions

C

No solution

D

None of these

Answer

Two solutions

Explanation

Solution

We have asin⁡A=bsin⁡B⇒sin⁡B=bsin⁡Aa=8sin⁡30∘7\frac { a } { \sin A } = \frac { b } { \sin B } \Rightarrow \sin B = \frac { b \sin A } { a } = \frac { 8 \sin 30 ^ { \circ } } { 7 }

= 47\frac { 4 } { 7 }

so that b > a > b sinA.

Hence angle B has two values given by sinB = 4/7