Give a general range of values for length BC.

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Expert Answers
flbyrne eNotes educator| Certified Educator

Sum of angles is = 180, so angle ABC = 180-58-62 = 60`@`

Applying law of Sines:

`(BC)/sin60 = 84/sin62 = 82/sin58`

BC=`84*sin60/sin62`=82.39

This is the only possible value.

llltkl | Student

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.

Thus, `(BC)/(sin60)=82/(sin58)=84/(sin62)`

`rArr BC=83.74` cm, which is definitely within this range.