Question

Name the smallest angle of ABC. The diagram is not to scale.

Answer 1

The smallest angle would be angle C. The reason why is because angle C is opposite of the shortest side (AB). The smallest angle in a traingle is opposite of the shortest side.

Answer 2

Answer-

The smallest angle of ABC is angle C.

Solution-

The sine law-

$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

As,

$=8$

$=AB$

$=c$

If, $\dfrac{a}{b}=\dfrac{c}{d},\ and\ b>d,\ then\ a>c$

If two fractions are equal in value and their denominator are decreasing, then the numerators must decrease in order to keep the value of the fraction same.

So, if $\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\ and\ c$, then

$\sin C$

As we know from the properties of trigonometry, if an angle is smaller than an another angle, then their sine will also smaller than the other.

i.e if $A$, then $\sin A$

So applying the same,

if $\sin C$, then $C$

Therefore, the smallest angle of ABC is angle C.