🔍 Key Concepts

• Relationship between altitude and zenith distance on the celestial sphere • The fact that a vertical circle from the horizon through the zenith is a right angle (90°) • How to convert between degrees and minutes when adding or subtracting angles

💭 Think About

• Think about how many degrees there are between the observer’s zenith (directly overhead) and the visible horizon. • If the Sun is 47° 50' above the horizon, how many degrees are left between the Sun and the point directly overhead? • When you subtract an angle with minutes from 90°, how do you handle the degrees and minutes carefully so you don’t make a borrowing mistake?

✅ Before You Answer

• Recall that altitude + zenith distance = 90° for a body above the horizon. • Carefully subtract 47° 50' from 90° 00', making sure you handle the minutes correctly (you may need to borrow 1° = 60'). • Verify that your final zenith distance is between 0° and 90° for a body that is clearly above the horizon.