Question 1: The height of a tree is times the length of its shadow. Find the angle of elevation of the sun.
Answer:
Let the length of the shadow
Therefore the height of the tree
Question 2: The angle of elevation of the top of a tower, from a point on the ground and at a distance of from its foot, is found to be
.Find the height of the tower.
Answer:
Let the height of the tower
Question 3: A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is from the wall and the ladder is making an angle of
with the ground. Find the height, up to which the ladder reaches.
Answer:
Let the height to which the ladder reaches
Distance from the base of the wall
Question 4: Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be and
respectively. Find the distance between them, if the height of the tower is
.
Answer:
Let the distance of the first person from the tower
Let the distance of the second person from the tower
Therefore the distance between the two persons
Question 5: A kite is attached to a sling. Find the length of the string, when the height of the kite is and the string make an angle
with the ground.
Answer:
Height of the kite
Let the length of the string
Question 6: A boy, tall, is
away from a tower and observes the angle of elevation of the top of the tower to be (i)
(ii)
. Find the height of the tower in each case.
Answer:
Case 1: Angle of elevation
Distance of the boy from the tower
Let the height of the tower
Hence the height of the tower
Case 2: Angle of elevation
Distance of the boy from the tower
Let the height of the tower
Hence the height of the tower
Question 7: The upper part of a tree, broken over by the wind, makes an angle of with the ground; and the distance from the root to the point where the top of the tree touches the ground, is
. What was the height of the tree before it was broken?
Answer:
Let the broken part of the tree is and the part of the tree still standing upright be
Hence the height of the tree before it was broken
Question 8: The angle of elevation of the top of an unfinished tower at a point distance from its base is
. How much higher must the tower be raised so that its angle of elevation at the same point may be
?
Answer:
Let the height of the unfinished structure
Let the tower be raised
Question 9: At a particular time when sun’s altitude is , the length of the shadow of altitude is a vertical tower is
. Calculate:
(i) the height of the tower,
(ii) the length of the shadow of the tower, when the sun’s altitude is same (b)
.
Answer:
Let the height of the tower
(i)
(ii) Let the shadow be when sun’s altitude is same
and
when sun’s altitude is
.
Question 10: The vertical poles are on either side of a road. A long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle
with the pole and when it is turned to rest against another pole, it makes angle
with the road. Calculate the width of the road.
Answer:
Let the distance of the foot of the ladder from the towers be and
For first tower, the angle of elevation
For first tower, the angle of elevation
Therefore the width of the road
Question 11: Two climbers are at points and
on a vertical cliff face. To an observer
,
from the foot of the cliff, on the level ground,
is at an elevation of
and
of
. What is the distance between the climbers?
Answer:
Let the climber be at height
and climber
be at
height
Therefore the distance between the two climbers
Question 12: A man stands away from a flag-pole. He observes that angle of elevation of the top of the pole is
and the angle of depression of the bottom of the pole is
. Calculate the height of the pole.
Answer:
Let the height of the top of the pole
Let the height of the bottom of the pole
The angle of elevation of the bottom of the pole = angle of elevation of the bottom of the pole
Hence the height of the pole
Question 13: From the top of a cliff height, the angle of depression of a buoy is
. Calculate, to the nearest meter, the distance of the buoy from the foot of the cliff.
Answer:
Angle of depression = angle of elevation
Let the distance of the buoy from the foot of the cliff