The angles of a triangle are in Ap.If the greatest angle eqal to the sum of the other two , then find the angles . Also find these angles are multiple of which angle.?

Question

Answer

Answer

First angle is 90degree , second angle is 60degree, and third angle is 30degree. The APs is 90,60,30. If greatest angle is 90 then it is equal to the sum of the both two other s.

Answer

Problem Statement: The angles of a triangle are in AP. If the greatest angle is equal to the sum of the other two, then find the angles. Also, find if these angles are multiples of which angle?

Solution:

Let's assume the angles of the triangle to be a, d and a + d.

Given, the greatest angle (a + d) is equal to the sum of the other two angles (a + d = a + (a + d)/2)

Solving the above equation, we get d = a/2.

Hence, the angles of the triangle are a, a/2 and 3a/2.

To find if these angles are the multiples of which angle, we need to find the common ratio of the given AP.

Let's assume the first term of the AP to be a and the common difference to be d.

We know that the third term of the AP is a + 2d = 3a/2.

Solving the above equation, we get d = a/2.

Hence, the common ratio of the AP is (a + d)/a = 3a/2a = 3/2.

Therefore, the angles of the triangle are multiples of 60 degrees (the common ratio of the AP is 3/2 which is a multiple of 60 degrees).

Hence, the angles of the triangle are a, a/2, and 3a/2 where a is a multiple of 60 degrees.

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