Question

The length of the sides of a triangle are $1.5,\frac{3\sqrt{3}}{2}$, and $3$, calculate the measure of the smallest angle of the triangle.

• A. $30$
• B. $40$
• C. $20$
• D. $60$

Answer 1

The correct option is A $30$

Let $a=1.5,b=\frac{3\sqrt{3}}{2},c=3$ be the sides of the triangle.

The smallest angle corresponds to that opposite the smallest side.

So, $\angle A$ is the smallest.

Using cosine rule, $\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\therefore \cos A=\frac{\frac{27}{4}+9-\frac{9}{4}}{9\sqrt{3}}$

$\therefore \cos A=\frac{\sqrt{3}}{2}$

$\therefore A=\frac{\pi }{6}={30}^o$