If `b=3,c=4,a n dB=pi/3,` then find the number of triangles that can be constructed.

Options

A. 0
B. 1
C. 2
D. Infinite

Answer

A

Explanation

Using `(b)/(sinB)=(c)/(sinC)`, we have
`sinC=(c)/(b) sinB=(4)/(3)xx(sqrt(3))/(2)=(2)/(sqrt(3))gt1`, which is not possible So, no triangle is possible.
(b) When A is an acute angle and a = b sin A.
In this case, only one triangle is possible which is right angled at B.
(c ) When A is an acute angle and ` a gt b` sin A.
In this case, there are two values of B given by sin B=`(bsinA)/(a)`, say `B_(1)` and `B_(2)` such that `B_(1)+B_(2)=180^(@)`.
Side c can be obtained by using c = `(asinC)/(sinA)`