Solve the equation `4costheta+5sintheta=5` if `tan51^(@)21^(')=5/4`

Explanation

To solve the equation \( 4 \cos \theta + 5 \sin \theta = 5 \) given that \( \tan(51^\circ 21') = \frac{5}{4} \), we can follow these steps:

### Step 1: Identify the angle \(\theta\)
Given that \( \tan(51^\circ 21') = \frac{5}{4} \), we can set \( \theta = 51^\circ 21' \).

### Step 2: Calculate \(\sin \theta\) and \(\cos \theta\)
Using the definition of tangent, we know:
\[
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