If \alpha is the angle between the line joining P and Q, and the line joining P and R, then what is \cos \alpha equal to ?
Consider the following for the next two (02) items that follow :<br>A hall is of length l, breadth b and height h. The maximum distance between any two points (say P and Q) inside the hall is 14 m, whereas the maximum distance between two points (say P and R) on the floor is 6\sqrt{5} m.
- A. \frac{2\sqrt{5}}{7}
- B. \frac{3\sqrt{5}}{7} ✓
- C. \frac{1}{3}
- D. \frac{2}{3}
Correct Answer: B. \frac{3\sqrt{5}}{7}
Explanation
The triangle PQR is a right-angled triangle with the right angle at R. The hypotenuse is the body diagonal PQ = 14, and the base is the floor diagonal PR = 6\sqrt{5}. Thus, \cos \alpha = \frac{PR}{PQ} = \frac{6\sqrt{5}}{14} = \frac{3\sqrt{5}}{7}.
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