Question

the angles of a triangle are in AP. the greatest angle is 84 degree. then find all the angles in radian.​

Answer 1

as all angles are in ap so let assuma it to be a-d ,a,a+d so total is

3a =180° a= 60°

the biggest angle is 84

the smallest angle is 36

the angle in radians are π/10`;

π/3` and 7π/15`

Answer 2

Given:

The angles of a triangle are in AP. The greatest angle is 84°.

To find:

All the angles in radian.

Solution:

The angles in radian, if the angles of a triangle are in AP, and the greatest angle is 84°, are $21\pi/45, \pi/3, \pi/5 \hspace{0.1cm} radians.$

We can solve the above mathematical problem using the following mathematical approach.

As the angles of the triangle are in Arithmetic progression, let the angles be a-2d, a-d, and a.

According to the question, the greatest angle is 84°.

⇒ a = 84°

The sum of all the angles in a triangle is 180°. So,

$a-2d+a-d+a = 180^\circ\\\\3a - 3d = 180^\circ\\\\3\times84^\circ -180^\circ= 3d\\\\d = \frac{72}{3} = 24^\circ\\\\ So, the angles are 84^\circ, (84-24)^\circ, and (84-2\times24)^\circ = 84^\circ, 60^\circ, 36^\circ.$

Angles in radian = $84\times\pi/180, 60\times\pi/180, 36\times\pi/180 = 21\pi/45, \pi/3, \pi/5 \hspace{0.1cm} radians.$

Therefore, the angles are $21\pi/45, \pi/3, \pi/5 \hspace{0.1cm} radians.$