Question

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

Answer 1

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)
${17}^2={28}^9,{15}^2=225,8^2=64$ (Finding the squares of the sides)
$289=225+64$ (Analyzing the squares of the sides)
${17}^2={15}^2+8^2$
$A{B}^2=A{C}^2+C{B}^2$
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, $\Delta ABC$ 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.
$\Rightarrow \angle ACB={90}^{\circ }$ and the right angle is the largest angle in a right triangle.
$\Rightarrow \angle ACB$ is the largest angle.
$\to$ Option A is correct.