Answer with explanation:
The triangle in the Diagram Described has following measurement:
Longest Side = 65 units
One side which can be either Perpendicular or base = 63 units
And , other side which can be also, either Perpendicular or base = 16 units
We can prove that the triangle described is right triangle by two ways.
1. Using Converse of Pythagorean Theorem
Square of Longest side = Sum of Squares of other two sides-----(1)
So, Square of Longest Side = 65²=4225
Sum of Square of other two sides = 16² + 63²
= 256 + 3969
= 4225
Statement (1), is valid.
So,Triangle is right angled triangle, right angled at A.
2. using Trigonometric Ratios
Suppose the triangle is right Angled at A.
In Right triangle B AC

B +C =90°
Also,→ ∠A + ∠B + ∠C=180°≡ (Angle sum property of triangle)
→∠A +90°=180°
→∠A=180° -90°
→∠A=90°
So, triangle is right Angled triangle , Right angled at A.
Hence ,proved.