Answer:
Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm
Explanation:
First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.
So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states
a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a
If we do this, it comes to the solution that a is approximately 4.00064cm.
Therefore, side b measures to 4.00064cm.