Question

the measures of the angles of a triangle are in A.p and greatest angle is 5 times the smallest. find the angles in degree and radians​

Answer 1

Answer:

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Step-by-step explanation:

Angles are in A.P. Let the angles of the triangle be a, a+d, a+2d

Sum of three angles is equal to 180.

a+a+d+a+2d=180

3a+3d=180

a+d=60 ——(1)

Smallest angle = a ; Greatest angle= a+2d

a+2d=5a

d=2a

From (1), a+2a=60

a=20

d=2(20)=40

Answer 2

The measures of the angles of a triangle are in Arithmetic progression and the greatest angle is 5 times the smallest.

We have to find the angles in degree and radians.

Let (a - d) , a and (a + d) be the angles of the given triangle, where (a - d) is smallest and (a + d) is greatest angles of the triangle.

We know,

“The sum of angles of a triangle equals to 180°.”

∴ (a - d) + a + (a + d) = 180°

⇒3a = 180°

⇒a = 60° ...(1)

A/C to question,

Greatest angle = 5 × smallest angle

⇒(a + d) = 5(a - d)

⇒a + d = 5a - 5d

⇒6d = 4a

⇒2a = 3d

⇒2 × 60° = 3d [ From equation (1), ]

⇒d = 40°

Hence angles are ; (60 - 40)° , 60° , (60 + 40)°

= 20° , 60° , 100°

Therefore the angles of triangle are 20° , 60° and 100°

Relation between degree and radian : π = 180°

so, 20° = π/9 radian

60° = π/3 radian

100° = 10π/18 radian

Therefore the angles of triangle in radian is π/9, π/3 and 10π/18.