Question

The ratio of the measures of the three angles in a tangle 3107. Find the measures of the angles and write them in size order,

largest:
middle

Answer 1

27, 90 and 63

Explanation:

Given

Ratio of triangle sides

`Ratio = 3 : 10 : 7`

Required:

The length of each side

Triangles in a triangle add up to 180.

The side with ratio 3 is:

`S_1 = (3)/(3 + 10 + 7) *180`

`S_1 = (3 *180)/(20)`

`S_1 = (540)/(20)`

`S_1 = 27`

The side with ratio 10 is:

`S_2 = (10)/(3 + 10 + 7) *180`

`S_2 = (10 *180)/(20)`

`S_2 = (1800)/(20)`

`S_2 = 90`

Lastly:

The side with 7 as its ratio

`S_3 = (7)/(3 + 10 + 7) *180`

`S_3 = (7 *180)/(20)`

`S_3 = (1260)/(20)`

`S_3 = 63`

Hence, the angles are: 27, 90 and 63