Quantitative Aptitude – Height and Distance
Height and distance is one of the very important topic of Quantitative Aptitude which frequently comes in competitive exams. To do a height and distance math problems you need to have a knowledge of Trigonometry. Here we will try to give you some basic idea about this topic and some formulas to do those maths. So let’s starts the discussion on height and distance.
What is Height and Distance ?
Definition: Finding measurement of any object from a certain point is called Distance and the vertical distance of an object is called Height.
Let’s explain this.
Sometimes we need to find out the height of a building, width of a sea, height of a tree etc. But these measurements are very tough to measure by any physical devices. You need trigonometric formulas to measure them with ease.
Suppose, we want to measure the height of a tree. We will not measure this by any devices. We use trigonometric formulas for this. Here comes two very important things of measuring heights, One is Angle of Elevation and other is Angle of Depression.
Assume that the man in the above picture is looking at the top of the tree. His eye level is “D”. Now as he look above his eye level here creates an angle (ox). This angle is called Angle of Elevation.
Similarly, when the man looking at the bottom at the tree, there also creates an angle. But now at the opposite side (oy). This angle is called Angle of Depression.
So, How we can find the height of a tree. The formula for this is-
Height = tan Θ X Distance between eye and tree
So, If we want to find the height of the tree we need to find out two things. One is “A” and another is “B”.
- A = tan ox X D
- B= tan oy X D
So, Height of the tree is: A + B
Some Important things to know:
- Sin θ = Perpendicular / Hypotenuse
- Cos θ = Base / Hypotenuse
- Tan θ = Perpendicular / Base
- Cosec θ = 1 / Sin θ
- Sec θ = 1 / Cos θ
- Cot θ = 1 / Tan θ
Values of T-ratios:
| θ | 0O | 30O (π/6) | 45O (π/4) | 60O (π/3) | 90O (π/2) |
| Sin θ |
0 | 1/2 | 1/√2 | √3/2 | 1 |
| Cos θ |
1 | √3/2 | 1/√2 | 1/2 | 0 |
| Tan θ |
0 | 1/√3 | 1 | √3 | Not Defined |
So, that’s all about basics of Height and Distance. Now if you have any questions on this topic then please let us know about that. We will discuss your thoughts here in www.AptitudeTricks.com. You can comment your questions and thoughts in the comment section below. We will get back to it as soon as possible.