_____________________HEIGHTS&DISTANCES_________________________________
- A tree breaks due to
the storms and the broken part bends so that the top of the tree touches
the ground making an angle 30° with the ground. The
distance from the foot of the tree to the point where the top touches the
ground is 10 metres. Find the height of the tree.
- A boy is standing on
the ground and flying a kite with 100 m of string at an elevation of 30°. Another boy is
standing on the roof of a 20 m high building and is flying his kite at an
elevation of 45°. Both the boy are on
opposite sides of both the kites. Find
the length of the string that the second boy must have so that the
two kites meet.
- The shadow of a
vertical tower on level ground increases by 10 metres, when the altitude
of the sun changes from 45° to 30°. Find the height of
the tower, correct to one place of decimal. ( take root 3 = 1.73
- A vertically straight
tree, 15 m high, is broken by the wind in such a way that its top just
touches the ground and makes an angle of 60° with the ground. At what height from the
ground did the tree break?
- The angle of elevation
of the top of a tower from a point A on the ground is 30°. On moving a distance
of 20 metres towards the foot of the tower to a point B the angle of
elevation increases to 60°. Find the height of
the tower and the distance of the tower from the point A.
- The angle of elevation
of an aeroplane from a point P on the ground is 60°. After a flight of 15 seconds,
the angle of elevation changes to 30°. If the aeroplane is
flying at a constant height of 1500 root 3 m, find the speed of the aeroplane.
- The angle of elevation,
q of a vertical tower
from a point on ground is such that its tangent is5/12 . On walking 192 metres towards the tower in the same
straight line, the tangent of the angle of elevation, is found to be 3/4 . Find the height of the tower.
- A man on the deck of a
ship is 16 m above water level. He observes that the angle of elevation of
the top of a cliff is 45° and the angle of
depression of the base is 30°. Calculate the
distance of the cliff from the shop and the height of the cliff.
- A round balloon of
radius a subtends an angle q at the eye of the
observer while the angle of elevation of its center is
. Prove that the height of the center of the balloon is
a sin cosec 
. - The shadow of a tower
is three times as long as the shadow of the tower when the sun says meet the ground at an angle of
60°. Find the angle
between the sun rays and the ground at the time of longer shadow.
- A ladder is placed against a wall such
that it just reaches the top of the wall. The foot of the ladder is 1.5 m
away from the wall and the ladder is inclined at an angle of 60° with the ground. Find
the height of the wall.
- A man is standing on
the deck of a ship, which is 8 m above water level. He observes the angle
of elevation of the top of a hill as 60° and the angle of depression of the base of the hill is 30°. Calculate the
distance of the hill from the ship and the height of the hill.
- From the foot of a
hill, the angle of elevation of the top of a tower is found to be 45°. After walking 2 km
upwards along the slope of the hill which is inclined at 30° , the same is found to
be 60°. Find the height of
the tower.
- There is a small island
is the middle of a 100 m wide river and a tall tree stands on the island.
P and Q are points directly opposite each other on the two banks and in
line with the tree. If the angles of elevation of the top of the tree from
P and Q are respectively 30° and 45°, find the height of
the tree.
