Question

The measures of the angles of a triangle are in the ratio of 2 : 5 : 8

a. find the measures of all three angles.
b. classify the triangle as acute, right, or obtuse.

Answer 1

Answer: The measures of all the three angles are 24 , 60 and 96

Step-by-step explanation:

`\\`Since the measures are given in ratio form, the first thing is to find the total ratio, which is

`\\`2 + 5+ 8 = 15

`\\`Recall that the sum of angles in a triangle is 180 ,so to calculate each angle , we have

`\\`2/15 x 180 = 24

`\\`also , 5/ 15 x 180 = 60

`\\`Finally, 8/15 x 180 = 96

`\\`The triangle is obtuse , since it is having one angle greater than 90.

`\\`It can not be acute because of the existence of 96 , for a triangle to be acute , all the angles must be less than 90 , and it can not be right triangle because there is no existence of 90