The Ratio of the Measures of the angles of a triangle is 3:4:8. FInd the measure of the largest triangle

Question

 help

Answer 1

The smallest angle is 3x, or 36°. The middle angle is 4x, or 48°.

36 + 48 + 96 = 180, which verifies the angles accurately describe a triangle.

36 = 3x

48 = 4x

96 = 8x

Since we know x = 12, clearly the ratio holds.

Answer 2

Since the angles are in the ratio 3:4:8, they have measures 3x, 4x, and 8x, for some positive number x.  

 

The angles of a triangle add up to 180°.

 

So, 3x + 4x + 8x = 180

 

                        15x = 180

 

                            x = 12

 

Measure of largest angle = 8x = 96°