Sum of angles is = 180, so angle ABC = 180-58-62 = 60`@`
Applying law of Sines:
`(BC)/sin60 = 84/sin62 = 82/sin58`
This is the only possible value.
Given `angle B` =`58^o` and `angle C` = `62^o`
Therefore, `angle A` =180-(58+62)=` 60^o`
According to the Rule of Proportionality, in every triangle, the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.
Here `angle C` is the largest angle(`62^o` ). So, AB is the longest side=84cm.
Meanwhile, `angle B` is the smallest angle(`58^o` ). So, AC is the shortest side=82cm.
This means that the third side, BC measures between 82 cm and 84 cm in length.
Therefore, the general range of values for length BC is `82 cm lt BC lt 84 cm` .
However, the exact value of side BC can be obtained from the law of sines of triangles.
`rArr BC=83.74` cm, which is definitely within this range.