Question

The angle of a triangle are in AP , such that the greatest is 5 times the least. Find the angle I. radian .​

Answer 1

Answer:

least be x

greatest 5x

middle 3x

9x=180

x=20

least angle is 20

middle angle is 60

largest angle is 100

Answer 2

Answer →

The angles of given triangle in radian are

$( { \frac{\pi}{9}) }^{c} .( { \frac{\pi}{3} )}^{c} .( { \frac{5\pi}{9} )}^{c}$

Solution →

Let the angles of triangle = a - d , a ,a+d

( As these are in A.P)

We know that sum of interior angle of triangle is 180° , then -

a-d + a + a+d = 180°

3a. = 180°

a. = 60°

Now according to the question, the relation between greatest and least angle is -

a+d = 5 ( a-d )

[ a+d > a-d ]

a+d = 5a -5d

5d + d = 5a - a

6d. = 4a

3d. =2a

From above we got a = 60°

3d. = 2(60)

d. = 2(60)/3

d. = 40°

So, the angle of∆ in degree measure are -

a - d = 60 -40

=> 20°

a. = 60°

a+d = 60 + 40

=> 100° .

Now , converting angles into radian , we know that multiplying degree measure by π/180° got converted into radian so -

20° = 20 × π/180°

20 =( π/9)radian .

60° = 60× π/180°

60° =( π/3)radian

100° = 100× π/180°

100° = (5π/9) radian.