If the sides of a triangle are in A.P. and the greatest angle of the triangle exceeds the least by `90^(@)`, then sine of the third angle is

Options

A. `(sqrt5)/4`
B. `(sqrt6)/4`
C. `(sqrt7)/4`
D. none of these

Explanation

To solve the problem step by step, let's denote the sides of the triangle as \( a \), \( b \), and \( c \), and the angles opposite to these sides as \( A \), \( B \), and \( C \) respectively.

### Step 1: Set up the sides in Arithmetic Progression (A.P.)
Since the sides of the triangle are in A.P., we can express them as:
- Let the sides be \( a = b - d \), \( b = b \), and \( c = b + d \) for some \( d > 0 \).

### Step 2: Identify the angles
According to the problem, the greatest angle \( A \) exceeds the least angle \( C \) by \( 90^\circ \):
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