Let n `in` Z and `DeltaABC` be a right tirangle with angle at C . If sin A and sin B are the roots of the quadratic equation `(5n + 8) x^(2) - (7n - 20) x + 120 = 0` , then find the value of n.

Explanation

To solve the problem, we need to find the value of \( n \) such that the roots of the quadratic equation \( (5n + 8)x^2 - (7n - 20)x + 120 = 0 \) are \( \sin A \) and \( \sin B \), where \( A \) and \( B \) are angles in a right triangle \( \Delta ABC \) with a right angle at \( C \).

### Step 1: Understand the properties of the triangle
In a right triangle, we know that:
\[ \sin A + \sin B = 1 \quad \text{(since \( A + B = 90^\circ \))} \]
\[
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