Height and Distance Aptitude Questions and Answers – Formulas and Quick Tricks
Angle of Elevation: The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer’s eye.
Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, angle of elevation is the angle between the horizontal and the line from the object to the observer’s eye (the line of sight).
That is, angle of elevation = ∠ AOP
Angle of Depression: If the object is below the level of the observer, then the angle between the horizontal and the observer’s line of sight is called the angle of depression.
Suppose a man from a point O looks down at an object P, placed below the level of his eye. Then, angle of depression is the angle between the horizontal and the observer’s line of sight.
That is, angle of depression = ∠ AOP
Angle Bisector Theorem
Consider a triangle ABC as shown above. Let the angle bisector of angle A intersect side BC at a point D. Then
(BD / DC) = (AB / AC)
(Note that an angle bisector divides the angle into two angles with equal measures.
That is., ∠BAD = ∠CAD in the above figure)
Basic Trigonometric Values
- Sin θ = (Perpendicular / Hypotenuse) = (AB / OB’)
- Cos θ = (Base/ Hypotenuse) = (OA/OB’)
- tan θ =(Perpendicular / Base) = (AB / OA’)
- Cosec θ = (1 / Sin θ) = (OB / AB’)
- Sec θ = (1 / Cos θ) = (OB / OA’)
- Cot θ = (1 / Tan θ) = (OA / AB’)
- sin2 θ + cos2 θ = 1.
- 1 + tan2 θ = Sec2 θ.
- 1 + cot2 θ = cosec2θ.
Height and Distance
Average Speed = Total Distance / Total Time
Total Distance Covered = 6 miles
Total Time = 45mins (0.75hrs)
Average Speed = 6/0.75 = 8miles/hrs
We know the rule that,
At particular time for all object, ratio of height and shadow are same.
Let the height of the pole be 'H'
Then, (18 / 8) = (H / 48)
H = 108m
From the right angle triangle
tan(45o) = x/375
x = 375m From
Let the distance between the towers be X
From the right angled triangle CFD
tan(45) = (90-45)/x
x = 45 meters
(180 - h) / 90 = tan(45)
h = 90m