# OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17

OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17. We Provide Step by Step Answer of Exe-17 with Self Evaluation and Revision of S Chand OP Malhotra Maths . Visit official Website CISCE for detail information about ICSE Board Class-10.

## OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17

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Exercise-17

### OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17

**Height and Distance :**

The directions of the objects can be described by measuring:

- Angle of elevation
- Angle of depression

Angles of elevation or angles of depression of the objects are measured by an instrument called **Theodolite**. Theodolite is based on the principles of trigonometry, which is used for measuring angles with a rotating telescope. In 1856, Sir George Everest first used the giant theodolite, which is now on display in the Museum of the survey of India in Dehradun.

**Heights and Distances :**

The most significant definitions that are used when dealing with heights and distances are given as:

**Definition 1:**The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.**Definition 2:**The angle of elevation of the point on the object (above horizontal level) viewed by the observer is the angle which is formed by the line of sight with the horizontal level.**Definition 3:**The angle of depression of the point on the object (below horizontal level) viewed by the observer is the angle which is formed by the line of sight with the horizontal level.

**To solve height and distance problems, trigonometric ratios for standard angles (Table 1) should be remembered.**

**Table 1: Trigonometric Ratios of Standard Angles :**

∠C | 0° | 30° | 45° | 60° | 90° |

sin C | 0 | ½ | 1/√2 | √3/2 | 1 |

cos C | 1 | √3/2 | 1/√2 | ½ | 0 |

tan C | 0 | 1/√3 | 1 | √3 | Not Defined |

cosec C | Not Defined | 2 | √2 | 2/√3 | 1 |

sec C | 1 | 2/√3 | √2 | 2 | Not Defined |

cot C | Not Defined | √3 | 1 | 1/√3 | 0 |

### Important Points :-

- In solving problems observer is represented by a point if his height is not given.
- In solving problems object is represented by a line segment and some times by a point if height or length is not considered.

- A line drawn parallel to earth surface is called horizontal line.
- The angle of elevation and depression are always acute angles.
- If the observer moves towards the objects like tower, building, cliff, etc. then angle of elevation increases and if the observer moves away from the object, the angle of elevation decreases.
- If the angle of elevation of sun decreases, then the length of shadow of an object increases and vice-versa.
- If in problems, the angle of elevation of an object is given, then we conclude that the object is at higher altitude than observer. The angle of depression implies that observer is at higher altitude than object.

Exercise-17

### OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17

#### Question 1:

The angle of elevation of the top ………………. height of tower.

#### Question 2:

A vertical flagstaff stand on a …………… find the height of the flag staff.

#### Question 3:

The string of a kite is 150 m …………… from the ground.

#### Question 4:

……………………..

………………………

……………………..

#### Question 25:

The of elevation of a ……….. find the height of cloud.

#### Question 26:

The angle of elevation of the top of a hill at the foot …………………… height of the hill.

### Self Evaluation And Revision

OP Malhotra Heights and Distances Class-10 S.Chand ICSE Maths Solutions Ch-17

#### Question 1:

From a window A 10 m above ground the angle …………… of the tower is metres.

#### Question 2:

In the figure ……………. length of PR.

#### Question 3:

…………………..

,……………………

……………………

#### Question 17:

The horizontal distance between two tower is 120 m …………………… significant figure.

#### Question 18:

An aeroplane at an altitude of 1500 m finds that two ships are ……………. find the distance between two ships.

— : End of Heights and Distances OP Malhotra S Chand Solutions :–

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