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

Answer:

The answer is False

Step-by-step 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

$3.5\neq 3.2$