Question

The angles of a triangle are in A. P. The number of grades in the least, is to the number of radians in the greatest as 40:¶.Find the angles in degrees.​

Answer 1

Explanation:

Given:-

The angles of a triangle are in A.P and

Number of grades in the least angles /number of radians in the greatest angle = 40/π

To Find:-

All the angles of triangle in degrees = ?

Formula used:-

Conversion of degree's into grades;

90°=100g

1° = (10/9)g

Solution:-

Let the angles of the traingle be (a-d),a,(a+d).

Then,

Sum = a - d + a + a + d = 180

= 3a = 180

= a = 180/3=60°

So the angles can be written as (60-d),60,(60+d).

Here the least angles is now (60-d)° and the greatest angle is (60+d)°.

On further solving we get,

Angles in grades as:

(60-d)→{10/9×(60-d)}g→(600-10d/9)g.

And in terms of radians, we have

(60+d)°= [(60+d)×π/180]c.

According to the question:-

Number of grades in the least angles /number of radians in the greatest angle =40/π

[(600-10d/9)/(60+d)π/180] = 40/π

So,

→ 600 - 10d = 120 + 2d

→ 12d = 480

→ d = 480/12

→ d = 40°

Therefore:-

The respective angles of the triangle are

(60-40)°,60°,(60+40)°= 20°,60° and 100°.