As per given by the question,
There are given that a length of three sides of the triangle.
The length of sides are, 14cm, 22cm, and 30cm.
Now,
For finding the measure of the smallest angle,
The smallest angle in a triangle is always opposite the shortest side. and also the bigest angle is always opposite the longest side.
So,
Suppose length A is 14cm, B is 22 cm and C is 30cm.
Then,
From the law of cosines,
Let A be the smallest angle.
So,
[tex]14^2=30^2+22^2-2(30)(22)\cos A[/tex]Now,
Find the value of angle A,
[tex]\begin{gathered} 14^2=30^2+22^2-2(30)(22)\cos A \\ 196=900+484-1320\cos A \end{gathered}[/tex]Now,
[tex]\begin{gathered} 196=1384-1320\text{ cosA} \\ 196-1384+1320\cos A=0 \\ -1188+1320\cos A=0 \\ -1188=-1320\cos A \\ \cos A=\frac{1188}{1320} \end{gathered}[/tex]Then,
[tex]\begin{gathered} \cos A=\frac{1188}{1320} \\ \cos A=0.9 \\ A=\cos ^{-1}(0.9) \\ A=25.84^{\circ} \end{gathered}[/tex]Hence, the measure of the smallest angle is 25.84 degree.
