# Height and Distance Questions

**FACTS AND FORMULAE FOR HEIGHT AND DISTANCE PROBLEMS**

**1.In a right angled**,where

**2. Trigonometrical Identities :**

**3. Values of T-ratios :**

**4. Angle of Elevation:**

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the angle of elevation of P as seen from O.

Angle of elevation of P from O is =

**5. Angle of Depression :**

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.

A) 21.6 m | B) 23.2 m |

C) 24.72 m | D) None of these |

Explanation:

Draw BE CD

Then, CE = AB = 1.6 m,

BE = AC =

CD = CE + DE = (1.6 + 20) m = 21.6 m.

A) 30 | B) 3000 |

C) 18 | D) 1800 |

Explanation:

If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.

Answer = 1800

A) Data inadequate | B) 8 units |

C) 12 units | D) None of these |

Explanation:

One of AB, AD and CD must have given.

So, the data is inadequate.

A) 173 m | B) 200 m |

C) 273 m | D) 300 m |

Explanation:

Let AB be the lighthouse and C and D be the positions of the ships.

A) 6 | B) 8 |

C) 9 | D) 10 |

Explanation:

Average speed = total distance / total time

Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours

Average speed = 6/ 0.75 = 8 miles/hour