Question

If the data given to construct a triangle ABC is a=5,b=7, $sinA=\frac{3}{4}$ then it is possible to construct

• A. Only one triangle
• B. two triangle
• C. infinitely many triangles
• D. No triangle

Answer 1

The correct option is D

No triangle

We have $\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$
$\Rightarrow \frac{\frac{3}{4}}{5}=\frac{sinB}{7}$
$\Rightarrow sinB=\frac{21}{20}>1$ (not possible)
Hence no triangle