Question

Which is the answer?

A: 19, 95, 114; obtuse

B: 10, 50, 60; acute

C: 16, 80, 96; obtuse

D: 12, 60, 72; acute

E: 15, 75, 90; right

Answer 1

Answer:  Choice E

15, 75, 90; right

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Explanation:

The ratio 1:5:6 scales up to x:5x:6x for some positive real number x.

The three interior angles are x, 5x and 6x. For any triangle, the interior angles always add to 180.

x+5x+6x = 180

12x = 180

x = 180/12

x = 15

So,

• 5x = 5*15 = 75
• 6x = 6*15 = 90

The triangle has angles of 15, 75 and 90 degrees.

Because we have a 90 degree angle, this is a right triangle.

Note how 15+75+90 = 180 to help confirm the answer.