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Question

In triangle ABC, if AC=15 inches,BA=17 inches, and CB=8 inches, then which angle will be the largest and what will be the measure of that angle?

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Solution

The length of the three sides of triangle ABC are AC = 15 in, AB = 17 in, and CB = 8 in.
17>15>8 (Arranging the sides in descending order)
172=289,152=225,82=64 (Finding the squares of the sides)
289=225+64 (Analyzing the squares of the sides)
172=152+82
AB2=AC2+CB2
We can observe that the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides.
Hence, ΔABC is a right triangle. (Using converse of the Pythagorean theorem)

AB is the hypotenuse and the angle opposite to the hypotenuse is a right angle.
ACB=90 and the right angle is the largest angle in a right triangle.
ACB is the largest angle.
Option A is correct.

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