Question

How do you find the longest side of a triangle if its triangle \[ABC\] and \[\angle A\] is \[70\] degrees \[\angle B\] is \[62\] degrees and \[\angle C\] is \[48\] degrees \[?\]

Answer 1

Hint: In this type of question we would compare all the angles given in the question and we would find the largest angle in degrees. Also, we need to draw a triangle with help of given angles in the question. The three angles are not equal. So, we have different lengths of sides in the triangle. By comparing the three different angles we can easily identify the largest side of a triangle \[ABC\] .

Complete step-by-step answer:
In this question, they give three different angles of a triangle. By using these angles we can draw the following figure.

From the above figure, we have the angle of \[A\] is \[{70^ \circ }\] , the angle of \[B\] is \[{62^ \circ }\] , and the angle of \[C\] is \[{48^ \circ }\] . By comparing these three angles we get,
 \[{70^ \circ } > {62^ \circ } > {48^ \circ }\]
So, the largest angle of a triangle is \[{70^ \circ }\] , the second largest angle of a triangle is \[{62^ \circ }\] and the minimum angle of a triangle is \[{48^ \circ }\] .
We know that the opposite side of the largest angle in a triangle will have the longest side of the triangle. Here we know that, \[\angle A\] is the largest angle, which is \[{70^ \circ }\] . So, the opposite side of \[\angle A\] is \[BC\] side.
So, the final answer is,
The longest side of the triangle \[ABC\] is \[BC\] the side.
So, the correct answer is “ \[BC\] ”.

Note: The opposite side of the largest angle would have the longest side of the triangle. To solve this type of question we would compare the given angles. If we want anyone's side value in \[cm\] , we would have at least one side value among the three sides of the triangle. Note that a triangle with a different angle must have a different length of sides.