### Eamcet - Maths - Heights Distances

A tower 51 m high has a mark at a height of 25m from the ground. If the two parts subtend equal angles to an eye at the height of 15 m from the ground, the distance of the tower from the observe is

A.  160 m

B.  150 m

C.  140 m

D.  none

The height of a hill is 3300 mt. From a point P on the ground the angle of elevation of the top of elevation of the top of the hill is 600. A balloon is moving with constant speed vertically upwards from P. After 5 minutes of its movement, a person sitting in it observes the angle of elevation of the top of the hill is 300. What is speed of the balloon?

A.  15.3 kmph

B.  24.5 kmph

C.  26.4 kmph

D.  32.3 kmph

A vertical pole consists of two portions, the lower being 1/3 rd of the whole. If the upper portion subtends an angle Tan-1 1/2 at a point in a horizontal plane through the foot of the plane and distance 40 ft. from it, then the height of the pole is

A.  36 ft

B.  35 ft

C.  40 ft

D.  none

Two pillars stand on a horizontal plane. A and B are two points on the line joining the bases of the pillars. The angles of elevation of the tops of the pillars as seen from Aare 300 and 600 and as seen from B are 600 and 450. If the length of AB is 30 mt, the heights of the pillars and the distance between them are

A.  100 (√3-1), 100 (√3+1), 100√3  mt

B.  15√3, 15(3+√3), 10(√3+1) mt

C.  25√3, 50, 75 mt

D.  10(2+√3), 27 (2+√3), 10(√3+1) mt

An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of two planes from the same point on the ground are 600 and 450 respectively. The height of the lower plane from the ground is

A.  100√3

B.  100/√3

C.  50

D.  150(√3+1)

The angle of the elevation of the top of a tower is 450 from a point 10 mt above the water level of a lake. The angle of depression of its image in the lake is 600. The height of the tower is

A.  10 (2+√3) mt

B.  27 (2+√3) mt

C.  10 (2-√3) mt

D.  75 (3+√3) mt

A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is

A.  20 m

B.  30 m

C.  40 m

D.  60 m

E.  20 m

A church tower AB standing on a level plane is surmounted by a spire BC of the same height as the tower. D is a point in AB such that AD=1/3AB. At a point on the plane 100 mt from the foot of the tower, the angles subtended by AD and BC are equal. The height of the tower is

A.  130 mt

B.  12 mt

C.  100 mt

D.  15 mt

Two pillars of equal height stand at a distance of 100 mt. At a point between them, the elevations of their tops are found to be 300 and 600. The height of the pillars and the position of the point of observation are

A.  100 (√3-1), 100 (√3+1) mt

B.  15√3, 15(3+√3) mt

C.  25√3 mt, 75 mt

D.  10(2+√3), 27 (2+√3) mt

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 300. After walking 120 metres towards it on level ground the elevation is found to be 600. Then the height of the object (in metres) is :

A.  120

B.  60√3

C.  120√3

D.  60

A man observes a tower AB of height h from a point P on the ground. He moves a distance ‘d’ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance 3d/4 in the same direction and the angle of elevation is three times that at P. Then 36h2=

A.  32d2

B.  35d2

C.  40d2

D.  42d2

At the foot of a mountain the angle of elevation of a summit is found to be 450. After ascending 1 km towards the mountain up, a slope of inclination 300, the angle of elevation is found to be 600. The height of the mountain is

A.  400(√2+2) mt

B.  500(√3+1) mt

C.  200(√2+1) mt

D.  100(√6+√2) mt

From the foot of a tower 220 m high the angle of elevation of the top of a hill is 600 and from the top of the tower the angle of depression of the top of the hill is 300. The height of the hill and the distance between them are

A.  165,55√3

B.  165,55

C.  65√3, 55

D.  165√3, 55√3

A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If α is the angle which the pole subtends at the midpoint of the opposite side, the length of each side of the park is

A.  (√3/2) h cot α

B.  (2/√3) h cot α

C.  (√3/2) h tan α

D.  (2/√3) h tan α