In triangle ABC, if AC=15inches,BA=17inches, and CB=8inches, 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.