Height and Distance Aptitude Questions & answer quantitative

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

Trigonometric Basic

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’)

Trigonometrical Identities:

sin² θ + cos² θ = 1.
1 + tan² θ = Sec² θ.
1 + cot² θ = cosec²θ.

Height and Distance Aptitude Questions and Answers With Detailed Explanation – Quantitative Aptitude

Height and Distance

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Question 1

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30^o and 45^o respectively. If the lighthouse is 100m high, the distance between the two ships is:

A	173m
B	200m
C	273m
D	300m

Question 1 Explanation:

Answer: Option C
Explanation:

Question 2

The angle of elevation of the sun when the length of the shadow of a pole is equal to the height of the pole is?

A	45^o
B	30^o
C	60^o
D	90^o

Question 2 Explanation:

Answer: Option B
Explanation:

Question 3

The angle of elevation of a ladder leaning against a wall is 60^o and the foot of the ladder is 4.6m away from the wall. The length of the ladder is:

A	2.3m
B	4.6m
C	7.8m
D	9.2m

Question 3 Explanation:

Answer: Option D
Explanation:

Question 4

The top of a 30m high wall makes an angle of elevation of 60^o with the top of a tower and makes an angel of depression of 45^o with the bottom of the tower. Find the distance between tower and wall?

A	27m
B	28m
C	29m
D	30m

Question 4 Explanation:

Answer: Option D
Explanation:

Question 5

From a point P on a level ground, the angle of elevation of the top tower is 30^o. If the tower is 100m high, the distance of point P from the foot of the tower is:

A	149m
B	156m
C	173m
D	200m

Question 5 Explanation:

Answer: Option C
Explanation:

Question 6

Jack takes 20mins to jog around the race course one time, and 25mins to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

A	6
B	8
C	9
D	10

Question 6 Explanation:

Answer: Option B
Explanation:
Average Speed = Total Distance / Total Time
Total Distance Covered = 6 miles
Total Time = 45mins (0.75hrs)
Average Speed = 6/0.75 = 8miles/hrs

Question 7

A vertical toy 18cm long casts a shadow 8cm long on the ground. At the same time a pole casts a shadow 48m, long on the ground. Then find the height of the pole?

A	181cm
B	180m
C	108m
D	118cm

Question 7 Explanation:

Answer: Option C
Explanation:
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

Question 8

From a point 375 meters away from the foot of a tower, the top of the tower is observed at an angle of elevation of 45^o, then the height (in meters) of the tower is?

A	375
B	450
C	225
D	250

Question 8 Explanation:

Answer: Option A
Explanation:

From the right angle triangle
tan(45^o) = x/375
x = 375m From

Question 9

The height of two towers are 90 meters and 45 meters. The line joining their tops make an angle 450 with the horizontal then the distance between the two towers is

A	22.5m
B	45m
C	60m
D	30m

Question 9 Explanation:

Answer: Option C
Explanation:

Let the distance between the towers be X
From the right angled triangle CFD
tan(45) = (90-45)/x
x = 45 meters

Question 10

The horizontal distance between two towers is 90m. The angular depression of the top of the first as seen from the top of the second which is 180m high is 450. Then the height of the first is