Important Formulas: Heights and Distance

# Important Formulas: Heights and Distance | Quantitative Aptitude (Quant) - CAT PDF Download

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.

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.

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## FAQs on Important Formulas: Heights and Distance - Quantitative Aptitude (Quant) - CAT

 1. How can I find the height of a building using the concept of trigonometry?
Ans. To find the height of a building using trigonometry, you can start by standing at a known distance from the building and measuring the angle of elevation from your eye level to the top of the building. Then, using the tangent function, you can calculate the height of the building by multiplying the distance from your position to the building by the tangent of the angle of elevation.
 2. Is there a formula to calculate the distance between two objects of known heights and their respective angles of elevation?
Ans. Yes, there is a formula to calculate the distance between two objects of known heights and their respective angles of elevation. You can use the formula: Distance = (Height of Object 2 - Height of Object 1) / (Tan(Angle of Elevation 1) - Tan(Angle of Elevation 2)). This formula is derived from the tangent function and allows you to find the distance between the two objects.
 3. Can the concept of heights and distances be applied to non-right angled triangles as well?
Ans. Yes, the concept of heights and distances can be applied to non-right angled triangles as well. By using the law of sines or the law of cosines, you can calculate the unknown sides or angles of a non-right angled triangle. These laws relate the ratios of the sides or angles of a triangle to each other and can be used to solve various trigonometric problems involving heights and distances.
 4. How can I determine the height of a tree without directly measuring it?
Ans. To determine the height of a tree without directly measuring it, you can use the concept of similar triangles and trigonometry. First, find a reference point some distance away from the tree where you can measure the angle of elevation to the top of the tree. Then, move closer to the tree and measure the angle of elevation again. By comparing the two angles and the distance you moved, you can set up a proportion and solve for the height of the tree.
 5. Is there a specific formula to calculate the angle of elevation?
Ans. No, there is no specific formula to calculate the angle of elevation. The angle of elevation is simply the angle between the horizontal line and the line of sight from an observer to an object that is above the horizontal line. It can be measured using a protractor or calculated indirectly by using trigonometric functions, such as the inverse tangent function, if the heights and distances are known.

## Quantitative Aptitude (Quant)

183 videos|152 docs|113 tests

### Up next

 Video | 13:17 min
 Test | 6 ques
 Doc | 11 pages
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