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Aptitude Height and Distance Concepts and Formulas

Points to Remember

1) Line of sight:

When we see an object, the line which joins our our eyes with the object is called the line of sight.

2) Angle of elevation:

When we see an object which is above the horizontal level of our eye, we have to raise our head to see the object. In this process, our eyes or line of sight moves through an angle which is called the angle of elevation.

See the image:

Apti Height and distance1

3) Angle of depression:

When we see an object which is below the horizontal level of our eye, we have to move our head downward to see the object. In this process, our eyes or line of sight moves through an angle which is called angle of depression.

See the image:

Apti Height and distance2

4) Tirgnometic ratios and their values:

θ30°45°60°90°
sinθ0½1/√2√3/21
cosθ1√3/21/√21/20
tanθ01/√31√3Not defined
cotθNot Defined√311/√30
secθ12/√3√22Not Defined
cosecθNot Defined2√22√31

Also remember:

Apti Height and distance4
Apti Height and distance5
Apti Height and distance6

5) Use of right angled triangle to solve problems:

Apti Height and distance7

In a right angled triangle ΔABC, where ∠C AB = 90° ∠ABC =θ, we have:

Apti Height and distance8

Also remember:

o sin2 θ + cos2θ= 1

o 1+ tan2 θ = sec2 θ

o 1+ cot2 θ = cosec2θ

6) Some important values to remember:

o √2 = 1.414

o √3 = 1.732

o √5 = 2.236

7) Pythagoras Theorem:

In a right-angled traiangle the square of the hypotenuse is equal to the sum of the squares of opposite sides or legs ( perpendicular and base).

(Hypotenus)2 = (Perpendicular)2 + (Base)2

Apti Height and distance9




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