Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window be 64 m, the distance between the two houses is:

A) 48 m
B) 36 m
C) 54 m
D) 72 m

Correct Answer:

A) 48 m

Description for Correct answer:
In \( \Large \triangle DAB, \tan \theta = \frac{64}{d} \)

\( \Large d = 64 \cot \theta \) ...(i)

In \( \Large \triangle CDE, \tan \left(90 ^{\circ} - \theta \right) = \frac{ \left(100 - 64\right) }{d} \)

\( \Large d = 36 \tan \theta \) ...(ii)

From Eqs. (i) and (ii), we get

\( \Large d^{2} = 36 \times 64 => d = 48 m\)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

Comments

Similar Questions

1). From the top of a light house 60 m high with its base at the sea level the angle of depression of a boat is \( \Large 15 ^{\circ} \). The distance of the boat from the foot of light house is:

A). \( \Large \left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)60 m \)

B). \( \Large \frac{\sqrt{3+1}}{\sqrt{3-1}} m \)

C). \( \Large \left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)60 m \)

D). none of therse

2). Two poles of equal heights stand on either side of a 100 m wide road. At a point between the poles the angles of elevation of the tops of the poles are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \). The height of each pole is:

A). 25m

B). \( \Large 25\sqrt{3} m \)

C). \( \Large \frac{100}{\sqrt{3}} m \)

D). none of these

3). At a distance 2h metre from the foot of a tower of height h meter the top of the tower and pole at the top of tower subtend equal angles. Height of the pole should be

A). \( \Large \frac{5h}{3} m \)

B). \( \Large \frac{4h}{3} m \)

C). \( \Large \frac{7h}{3} m \)

D). \( \Large \frac{3h}{3} m \)

4). A kite is flying at an inclination of \( \Large 60 ^{\circ} \) with the horizontal. If the length of the thread is 120 m, then the height of the kite is:

A). \( \Large 60\sqrt{3} m \)

B). 60 m

C). \( \Large \frac{60}{\sqrt{3}} m \)

D). 120 m

5). If a flag staff of 6 m high placed on the top of a tower throws a \( \Large 2\sqrt{3} m\) along the ground, then the angle (in degrees) that the sun makes with the ground is:

A). \( \Large 60 ^{\circ} \)

B). \( \Large 80 ^{\circ} \)

C). \( \Large 75 ^{\circ} \)

D). none of these

6). The angle of elevation of the top of a tower from a point A due south of it, is \( \Large \tan^{-1}6 \) and that from B due west of it, is \( \Large \tan^{-1}7.5 \). If h is the height of the tower, then AB = xh, where \( \Large x^{2} \) is equal to:

A). \( \Large \frac{21}{700} \)

B). \( \Large \frac{42}{1300} \)

C). \( \Large \frac{41}{900} \)

D). none of these

7). An observer standing on a 300 m high tower obeserver see two boat in the same direction, their angles of depression are \( \Large 60 ^{\circ} \) and \( \Large 30 ^{\circ} \) respectively. The distance between boats is:

A). 173.2 m

B). 346.4 m

C). 25 m

D). 72 In

8). A pole stands vertically inside a triangular par ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then is park the foot of the pole is at the:

A). centroid

B). circumcentre

C). incentre

D). ortho centre

9). The angle of elevation of the top of the tower observed from each of the three points A, B, C on the ground forming a triangle is the same angle \( \Large \alpha \). If R is the circumradius of the triangle ABC, then the height of the tower is

A). \( \Large R \sin \alpha \)

B). \( \Large R \cos \alpha \)

C). \( \Large R \cot \alpha \)

D). \( \Large R \tan \alpha \)

10). From of 60 m high tower angles of depression of the top and bottom of a house are \( \Large \alpha \) and \( \Large \beta \) respectively. If the height of the house is \( \Large \frac{60 \sin \left( \beta - \alpha \right) }{x} \) is equal, then x:

A). \( \Large \sin \alpha \sin \beta \)

B). \( \Large \cos \alpha \cos \beta \)

C). \( \Large \sin \alpha \cos \beta \)

D). \( \Large \cos \alpha \sin \beta \)