# 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: 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: 4) Tirgnometic ratios and their values:

 θ 0° 30° 45° 60° 90° sinθ 0 ½ 1/√2 √3/2 1 cosθ 1 √3/2 1/√2 1/2 0 tanθ 0 1/√3 1 √3 Not defined cotθ Not Defined √3 1 1/√3 0 secθ 1 2/√3 √2 2 Not Defined cosecθ Not Defined 2 √2 2√3 1

Also remember:   5) Use of right angled triangle to solve problems: In a right angled triangle ΔABC, where ∠C AB = 90° ∠ABC =θ, we have: 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    