HEIGHT AND DISTANCE (CDS)

Total Questions: 24

1. The angles of elevation of the tops of two pillars of heights h and 2h from a point P on the line joining the feet of the two pillars are complementary. If the distances of the foot of the pillars from the point P are x and y respectively, then which one of the following is correct? [2019 (II) Evening Shift]

Correct Answer: (c) 2h² = xy
Solution:


2. A plane is going in circles around an airport. The plane takes 3 min to complete one round. The angle of elevation of the plane from a point P on the ground at time t is equal to that at time (t + 30) s. At time (t + x) s, the plane flies vertically above the point P. What is x equal to? [2019 (I) Morning Shift]

Correct Answer: (c) 105 s
Solution:“A” is airport and a plane is going in circles around it.



3. Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30°, and the angle of elevation to the top of the tower at C is 45°. What is the ratio of the height of towers at B and C? [2019 (I) Morning Shift]

Correct Answer: (b) 1 : 3
Solution:A regular hexagon ABCDEF.



4. On the top of a hemispherical dome of radius r, there stands a flag of height h. From a point on the ground, the elevation of the top of the flag is 30º. After moving a distance d towards the dome, when the flag is just visible, the elevation is 45º. The ratio of h to r is equal to [2018 (II) Evening Shift ]

Correct Answer: (a)
Solution:According to given information, we have the following figure.


5. Each corner of a square subtends an angle of 60° at the tip of a tower of height h m standing at the centre of the square. If l is the length of each side of the square, then what is h² equal to ? [2018 (I) Morning Shift]

Correct Answer: (c) 3l²/2
Solution:Let ABCD be a square

6. From a height of h units, a man observes the angle of elevation as α and angle of depression as β of the top and the bottom respectively of a tower of height H (> 4h). To what further height should he climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower? [2018 (I) Morning Shift]

Correct Answer: (b) H− 2h units
Solution:Let the distance between two towers be ‘a’ units.



7. Let AB represents a building of height h metre with A being is top, B being its bottom. Let A' B' represents a tower of height (h + x) metre (x > 0) with A' being its top and B' being its bottom. Let B B' = d metre. Let the angle of elevation of A' as seen from A be 45°. [2017 (II) Evening Shift]

Consider the following statements.
Statement I : h + x > d
Statement II : The angle of depression of B as seen from A' is less than 45°.

Which one of the following is correct in respect of the above statements?

Correct Answer: (c) Statement I is true but Statement II is false
Solution:We have, AB = h


8. A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N α° E on the opposite parallel bank. He than walks 200 m along the bank to the point Y towards East, and finds the tower to be N Wβ° . From these observations, the breadth of the river will be (Given that tanα° = 2 and tan . β° = 0 5) From [2017 (II) Evening Shift]

Correct Answer: (c) 80 m
Solution:Let,

9. An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60º and 45º respectively. What is the height of the lower plane from the ground? [2017 (I) Morning Shift]

Correct Answer: (a) 100√3 m
Solution:Let the height of the lower plane from the ground be h m and PA = x


10. From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30º and 45º respectively. What is the height of the tree? [2017 (I) Morning Shift]

Correct Answer: (b) 90 − 30√3 m
Solution: