Question

In triangle ABC angle a=x b=3x C=y if 3y-5x=30 prove that triangle is right angled

Answer 1

∠a = x
∠b = 3x
∠c = (30+5x)/3

If it's a right triangle, then only one of the angles is 90°
If one angle is 90° then the sum of the two other angles is also 90°

If ∠a is the right angle
∠b + ∠c = 90°
3x + (30+5x)/3 = 90°

Since ∠a = x = 90°
3(90°) + (30+5(90°))/3 = 90°
270° + 480°/3 = 90°
But 430° ≠ 90°

This means that ∠a ≠ 90°

Now, if ∠b is the right angle
∠a + ∠c = 90°
=>x + (30+5x)/3 = 90°

So,since ∠b = 3x = 90°
=>x = 90° /3 = 30
30° + (30+5(30°))/3 =?= 90°
30° + (30+150°)/3 =?= 90°
90° = 90°

Then ∠b = 90° and ∆ABC is a right triangle.