SAT Mathematics - Height and Distance
Exam Duration: 45 Mins Total Questions : 25
The angle of elevation of the top of a tree from a point at a distance of 200 m from its base is 60°. The height of the tree is
- (a)
\(50\sqrt { 3 } m\)
- (b)
\(100\sqrt { 3 } m\)
- (c)
\(200\sqrt { 3 } m\)
- (d)
\(\frac { 200 }{ \sqrt { 3 } } m\)
An aeroplane flying horizontally 1km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°. The uniform speed of the aeroplane is
- (a)
240kmph
- (b)
240\(\sqrt { 2 } \) kmph
- (c)
240 \(\sqrt { 3 } \) kmph
- (d)
none of these
The angle of elevation of a cloud at a height h above the level of water in a lake is \(\alpha\) and the angle of depression of its image in lake is \(\beta\) . Then, the height of the cloud above the surface of the lake is
- (a)
h cot \(\beta\)
- (b)
h(cot\(\alpha\) + cot \(\beta\))
- (c)
h cot \(\alpha\)
- (d)
\(h\left( \frac { cot\alpha +cot\beta }{ cot\alpha -cot\beta } \right) \)
A flagstaff of 5m high stands on a building of 25m height. An observer finds at a height of 30m, the flagstaff and the building subtend equal angles. The distance of the observer from the top of the flagstaff is
- (a)
5m
- (b)
\(5\sqrt { 3 } m\)
- (c)
\(5\sqrt { \frac { 3 }{ 2 } } m\)
- (d)
none of these
If a flagstaff 6m high is placed on the top of a tower throws a shadow of 2\(\sqrt { 3 } \) m along the ground, then the angle that the seen makes with the ground is
- (a)
60°
- (b)
30°
- (c)
90°
- (d)
none of these
A man on the top of a tower, standing on the sea-shore. finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30° and 60°, How soon will the boat reach the sea-shore?
- (a)
5 minute
- (b)
10 minute
- (c)
\(\sqrt { 3 } \) minute
- (d)
None of these
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will take the car to reach the observation tower?
- (a)
14 min 35 sec
- (b)
15 min 49 sec
- (c)
16 min 23 sec
- (d)
18 min 5 sec
There are two temples, one on each bank of a river,just opposite to each other. One temple is 54m high. From the top of this temple, the angles of depression of the top and the foot of the other'temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.
- (a)
31.14 m, 18 m
- (b)
11.14 m, 18 m
- (c)
21.14 m, 17 m
- (d)
none of these
A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 36m from the bank, he finds the angle to be 30°. Find the breadth of the river.
- (a)
15 m
- (b)
16 m
- (c)
17 m
- (d)
18 m
The angular elevation of a tower from a point is 30°, at a point in a horizontal line to the foot of the tower and 100 metres nearest is 60°, find the height of the tower. Find the distance of the first point from the tower.
- (a)
\(50\sqrt { 3 } ,\quad 150m\)
- (b)
\(40\sqrt { 3 } ,\quad 140m\)
- (c)
\(30\sqrt { 3 } ,\quad 130m\)
- (d)
none of these
What is the angle of elevation of the sun when the length of the shadow of a pole is .\(\sqrt { 3 } \) times the height of the pole?
- (a)
10\(°\)
- (b)
20\(°\)
- (c)
40\(°\)
- (d)
30\(°\)
A man sitting in an aeroplane observes that the angle of depression of two temples 2 km apart are 60°, If the plane is exactly above the middle point of the line joining the temples, what its height?
- (a)
\(\sqrt { 1 } km\)
- (b)
\(\sqrt { 2 } km\)
- (c)
\(\sqrt { 4 } km\)
- (d)
\(\sqrt { 3 } km\)
The angle of depression of a boat B from the top k of cliff HK, 300 metres high, is 40°. Find the distance of the boat from the foot H of the cliff.
- (a)
158 m
- (b)
258 m
- (c)
358 m
- (d)
none of these
A ladder leaning against a wall makes an angle of 60° with the ground. If the length of the ladder is 19m, find the distance of the foot of the ladder from the wall.
- (a)
10.5 m
- (b)
8.5 m
- (c)
9.5 m
- (d)
none of these
From a point P on a level ground, the angle of elevation of the top of a tower is 30°, if the tower is 100m high, the distance of point P from the foot of the tower is
- (a)
149 m
- (b)
156 m
- (c)
173 m
- (d)
200 m
An observer 1.6m tall is \(20\sqrt { 3 } \) m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is
- (a)
21.6 m
- (b)
23.2 m
- (c)
24.72 m
- (d)
none of these
The angles of elevation of the top of a building and the top of chimney on the roof of the building from a point on the ground are x and 45° respectively. The height of building is h meter. Then the height of the chimney, in metre is?
- (a)
h cot x+h
- (b)
h cot x-h
- (c)
h tan x-h
- (d)
h tan x+h
Two poles of equal heights are standing opposite to each other on either side of a road which is 100m wide. From a point between them on road, angles of elevation of their top are 30° and 60°. The height of each pole in metre is
- (a)
\(25\sqrt { 3 } \)
- (b)
\(20\sqrt { 3 } \)
- (c)
\(28\sqrt { 3 } \)
- (d)
\(30\sqrt { 3 } \)
If the angle of elevation of the sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is
- (a)
\(20\left( \sqrt { 3 } -1 \right) m\)
- (b)
\(20\left( \sqrt { 3 } +1 \right) m\)
- (c)
\(10\left( \sqrt { 3 } -1 \right) m\)
- (d)
\(10\left( \sqrt { 3 } +1 \right) m\)
One flies a kite with a thread 150 metre long, If the thread of the kite make an angle of 60°, with the horizontal line, then the height of the kite from the ground (assuming the thread to be a straight line) is
- (a)
50m
- (b)
75\(\sqrt { 3 } m\)
- (c)
25\(\sqrt { 3 } m\)
- (d)
80m
The string of a kite is 150 metres long and it makes an angle of 60° with the horizontal. Find the height of the kite from the ground
- (a)
75\(\sqrt { 3 } \)m
- (b)
75\(\sqrt { 2 } \)m
- (c)
50\(\sqrt { 3 } \) m
- (d)
50\(\sqrt { 2 } \) m
Find the angle of elevation of the top of a tower of height 100\(\sqrt { 3 } \) m from a point at a distance of 100 m from the foot of the tower on a horizontal plane
- (a)
45°
- (b)
60°
- (c)
75°
- (d)
30°
The angle of elevation of a tower at a point is 45°. After going 40m towards the foot of the tower, the angle of elevation of the tower becomes 60°. Find the height of the tower.
- (a)
\(\frac { 40\sqrt { 3 } }{ \sqrt { 3 } +1 } m\)
- (b)
40\(\sqrt { 3 } m\)
- (c)
\(\frac { 40\sqrt { 3 } }{ \sqrt { 3 } -1 } m\)
- (d)
none of these
From the top of buildiitg 30m high, the top and bottom of a tower are observed to have angles of depression 30° and 45° respectively. Find the height of the tower
- (a)
\(30\left( 1+\frac { 1 }{ \sqrt { 3 } } \right) m\)
- (b)
\(30\left( 1-\frac { 1 }{ \sqrt { 3 } } \right) m\)
- (c)
\(30\left( 2+\frac { 1 }{ \sqrt { 3 } } \right) m\)
- (d)
\(30\left( 2-\frac { 1 }{ \sqrt { 3 } } \right) m\)
The angle of elevation of the moon when the length of the shadow of a pole is equal to its height is
- (a)
60°
- (b)
45°
- (c)
90°
- (d)
30°
