Question

If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest side of the triangle is _____. 3.2 3.5 2.3 2.6

Answer 1

3.5

Explanation:

We can use the cos rule to solve this type of problem. The cos rule is given by:

`p^2=a^2 + b^2 -2ab CosP`

Where p is the side opposite of the "in-between" angle given and P is the angle given between 2 sides. Also, a and b are the 2 sides given (adjacent to the angle).

So, here, "p" is what we want to find (smallest side is opposite of smallest angle). And, a and b are 4 & 7 respectively. P is 20 degrees.

Now, using Cos Rule:

`p^2=a^2 +b^2 - 2abCosP\\p^2=4^2+7^2-2(4)(7)Cos20\\p=3.5`

So, the smallest side, p, is 3.5