Right Angle Hands
Right Angle Between Hands problems ask for the times when the hour and minute hands of a clock are perpendicular to each other (form a 90° angle). These problems test your ability to solve time equations using the angle formula.
What You'll Learn
Introduction to Right Angle Hands
Right Angle Between Hands problems ask for the times when the hour and minute hands of a clock are perpendicular to each other (form a 90° angle). These problems test your ability to solve time equations using the angle formula.
Prerequisites
How to Solve Right Angle Hands Problems
Step 1: Set up the equation |30H - 5.5M| = 90
Step 2: Solve for M in terms of H: M = (30H ± 90)/5.5
Step 3: For each hour H (1 to 11), calculate both solutions
Step 4: Keep only solutions where 0 ≤ M < 60
Step 5: For each valid solution, format as H:MM
Step 6: For H=12, treat as H=0 in calculations
Step 7: Answer with the time(s) when hands are at right angle
Example Problem
Example: At what time between 3:00 and 4:00 are the hands at right angles? Solution: Step 1: H = 3, |30×3 - 5.5M| = 90 → |90 - 5.5M| = 90 Step 2: Case 1: 90 - 5.5M = 90 → -5.5M = 0 → M = 0 (3:00) Step 3: Case 2: 90 - 5.5M = -90 → -5.5M = -180 → M = 180/5.5 = 32.727 ≈ 33 minutes Step 4: 3:00 is the start (not between 3-4), so answer is 3:33 Answer: Approximately 3:33
Pro Tips & Tricks
- Between H and H+1, there are exactly two right angle positions
- The first occurs at M = (30H - 90)/5.5 (if positive)
- The second occurs at M = (30H + 90)/5.5 (if < 60)
- At 3:00, the hands are at 90° (hour at 90°, minute at 0°)
- At 9:00, the hands are at 90° (hour at 270°, minute at 0°)
- Right angles occur 22 times in 12 hours
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Right Angle Hands. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Right Angle Hands is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Right Angle Hands?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: