Question

Angles of triangle are in A.P. If the number of degrees in the smallest to the number of radians in the largest is as 60:π, then the smallest angle is

Answer 1

$\huge{ \red{➩}}$

Let the angles of the triangle are (a - d), a, (a + d)

Now, in a triangle, the sum of all angles equal to 180 degree

=> (a - d) + a + (a + d) = 180

=> a - d + a + a + d = 180

=> 3a = 180

=> a = 180/3

=> a = 60

Now, the angle are (60 - d), 60, (60 + d)

Now, 60 - d is the least and 60 + d is the greatest angle.

Now, (60 + d)° = {(60 + d) * (π/180)}c

Given that, ➩number of radians in the greatest angle/number of degrees in the least one = π/60

=> {(60 + d) * (π/180)}c /(60 - d) = π/60

=> (60 - d)/{(60 + d) * (π/180)}c = 60/π

=> 180(60 - d)/{(60 + d) * π} = 60/π

=> 180(60 - d)/(60 + d) = 60

=> (60 - d)/(60 + d) = 60/180

=> (60 - d)/(60 + d) = 1/3

=> 3(60 - d) = (60 + d)

=> 180 - 3d = 60 + d

=> 180 - 60 = 3d + d

=> 4d = 120

=> d = 120/4

=> d = 30

➩Now, the angles are (60 - 30), 60, (60 + 30) = 30, 60, 90

Answer 2

Step-by-step explanation:

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Class 11

MATHS

MEASUREMENT OF ANGLES

Updated On: 6-11-2020

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The angles of a triangle are in AP and the ratio of the number of degrees in the least to the number of radians in the greatest is

. Find the angles in degree and radians.

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Text Solution

Solution :

Let the angles of the triangle be

and

. Then , <br>

. <br> Thus, the angleare

and

. <br> Number of degrees in the least angle

. <br> Number of radians in the greatest angle

. <br>

. <br>

<br>

. <br>

The required angles are

and

, i.e.,

and

.<br> These angles in radians are <br>

, i.e.,

.