# Step-by-Step Solution Given: **Altitude angle:** \( 35^\circ 26' 23'' \) We are asked for the **equivalent zenith angle**. --- ## 1. Understanding Definitions - **Altitude angle** (\( h \)): The angle above the horizon. - **Zenith angle** (\( z \)): The angle from the zenith (directly overhead) down to the object. **Relationship:** \[ z = 90^\circ - h \] --- ## 2. Convert Altitude Angle to Decimal Degrees Given: - Degrees: \( 35^\circ \) - Minutes: \( 26' \) - Seconds: \( 23'' \) \[ \text{Decimal Degrees} = 35 + \frac{26}{60} + \frac{23}{360} \] Calculate each part: - \( \frac{26}{60} = .433333 \) - \( \frac{23}{360} \approx .006389 \) Sum: \[ 35 + .433333 + .006389 = 35.439722^\circ \] --- ## 3. Calculate Zenith Angle \[ z = 90^\circ - 35.439722^\circ = 54.560278^\circ \] --- ## 4. Convert to Degrees, Minutes, Seconds ### a) Degrees - Degrees: \( 54^\circ \) ### b) Minutes - \( .560278 \times 60 = 33.61668 \) - Minutes: \( 33' \) ### c) Seconds - \( .61668 \times 60 \approx 37.0008 \) - Seconds: \( 37'' \) (rounded to nearest second) --- ## 5. Final Answer \[ \boxed{54^\circ\,33'\,37''} \] --- ## Summary Table | Quantity | Value | |----------------------|---------------------| | Altitude angle (\(h\)) | \(35^\circ\,26'\,23''\) | | Zenith angle (\(z\)) | \(54^\circ\,33'\,37''\) | --- **Final Answer:** The equivalent zenith angle is **\(54^\circ\,33'\,37''\)**.