Question

If the smallest angle of a triangle is 20 degrees and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest side of the triangle is 3.2 - true or false?

Answer 1

Hello,
Al 'Kashi theorem says:

a²=4²+7²-2*4*7*cos 20°=12.37721...
==>a=3.518126381...≈3.5 ==>False.

Answer 2

The answer is False

Explanation:

we know that

Applying the law of cosines, find the length of the third side of the triangle

`c^(2)= a^(2)+b^(2)-2abcos(C)`

In this problem we have

`a=4\ units, b=7\ units, C=20\°`

substitute the values and solve for c

`c^(2)= 4^(2)+7^(2)-2*(4*7)*cos(20\°)`

`c= 3.5\ units` -------> smallest side of the triangle

therefore

`3.5\\eq 3.2`