If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

examrobotsa's picture

Submitted by examrobotsa on

Q: 141 (IAS/1999)
If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,11,17,3,6,8,11

keywords: 

{'angles': [0, 1, 1, 0], 'triangle': [0, 1, 0, 1], 'angle': [0, 0, 1, 0], 'right triangle': [0, 1, 0, 0], 'ratio': [1, 0, 1, 12]}

To determine the nature of the triangle based on the given ratio of angles, we need to consider the sum of the angles in a triangle, which is always 180 degrees.

Let`s denote the angles of the triangle as 4x, 3x, and 2x, where x is a constant.

According to the given ratio, we have:

4x + 3x + 2x = 180

Simplifying the equation, we get:

9x = 180

Dividing both sides by 9, we find:

x = 20

Now, we can substitute the value of x back into the angles:

Angle 1 = 4x = 4 * 20 = 80 degrees

Angle 2 = 3x = 3 * 20 = 60 degrees

Angle 3 = 2x = 2 * 20 = 40 degrees

Based on these angles, we can conclude that the triangle is acute, meaning all angles are less than 90 degrees. Therefore, the correct option is "is acute."

Practice this on app