CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 9 - MCQExams.com

The angle of elevation of a ladder leaning against a wall is $$60^{\circ}$$ and the foot of the ladder is $$4.6\ m$$ away from the wall. The length of the ladder is:
  • $$2.3\ m$$
  • $$4.6\ m$$
  • $$7.8\ m$$
  • $$9.2\ m$$
A man standing at a point P is watching the top of a tower, which makes an angle of elevation of $$30^{\circ}$$ with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes $$60^{\circ}$$. What is the distance between the base of the tower and the point P?
  • $$4\sqrt {3} units$$
  • $$8\ units$$
  • $$12\ units$$
  • Data inadequate
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are $$30^{\circ}$$ and $$45^{\circ}$$ respectively. If the lighthouse is $$100\ m$$ high, the distance between the two ships is:
  • $$173\ m$$
  • $$200\ m$$
  • $$273\ m$$
  • $$300\ m$$
The length of shadow of a tree is $$16\ m$$ when the angle of elevation of the sun is $$60^{\circ}$$. What is the height of the tree?
  • $$8$$ m
  • $$16$$ m
  • $$16\sqrt {3}$$ m
  • $$\dfrac {16}{\sqrt {3}}$$ m
A building that is 150 ft tall casts a shadow of 20 feet long. At the same time a tree casts a shadow of 2 ft. How tall is the tree?
  • 10
  • 15
  • 20
  • 25
  • 30
The ramp for unloading a moving truck, has an angle of elevation of $$30^{\circ}$$. If the top of the ramp is $$0.9$$m above the ground level, then find the length of the ramp.
  • $$1.8\ m$$
  • $$1\ m$$
  • $$0.8\ m$$
  • None of these
To find the cloud ceiling, one night an observer directed a spotlight vertically at the clouds. Using a theodolite placed $$100\text{ m}$$ from the spotlight and $$1.5$$m above the ground, he found the angle of elevation to be $$60^{\circ}$$. How high was the cloud ceiling? ( Hint : See figure) 
( Note : Cloud ceiling is the lowest altitude at which solid cloud is present. The cloud ceiling at airports must be sufficiently high for safe take offs and landings. At night the cloud ceiling can be determined by illuminating the base of the clouds by a spotlight pointing vertically upward.) 
622312_a73e61f94dd842029d8f41d4a6fc7265.png
  • $$174.7\text{ m}$$
  • $$14.7\text{ m}$$
  • $$147.7\text{ m}$$
  • None of these
A person $$X$$ standing on a horizontal plane, observes a bird flying at a distance of $$100\ m$$ from him at an angle of elevation of $$30^{o} $$. Another person $$Y$$ standing on the roof of a $$20$$m high building, observes the bird at the same time at an angle of elevation of $$45^{o}$$. If $$X$$ and $$Y$$ are on the opposite sides of the bird, then find the distance of the bird from $$Y$$. 
  • $$30\sqrt{2}m$$
  • $$20\sqrt{2}m$$
  • $$30\sqrt{3}m$$
  • $$None\ of\ these$$
A person in a helicopter flying at a height of $$700$$m, observes two objects lying opposite to each other on either bank of a river. The angles of depression of the objects are $$30^{\circ}$$ and $$45^{\circ}$$ respectively. Find the width of the river. $$\left ( \sqrt{3}=1.732 \right )$$
  • $$1.9\ km$$
  • $$1.4\ km$$
  • $$2.1\ km$$
  • None of these
A lamp-post stands at the centre of a circular park. Let $$P$$ and $$Q$$ be two points on the boundary such that $$PQ$$ subtends and angle $$90^{\circ}$$ at the foot of the lamp-post and the angle of elevation of the top of the lamp post from $$P$$ is $$30^{\circ}$$. If $$PQ=30$$ m, then find the height of the lamp post. 
  • $$5\sqrt 6$$ m
  • $$4\sqrt 6$$ m
  • $$6\sqrt 5$$ m
  • $$8\sqrt 3$$ m
The angles of elevation of an artificial earth satellite is measured from two earth stations, situated on the same side of the satellite, are found to be $$30^{\circ}$$ and $$60^{\circ}$$. The two earth stations and the satellite are in the same vertical plane. If the distance between the earth stations is $$4000$$ km, find the distance between the satellite and earth. $$\left ( \sqrt{3}=1.732 \right )$$
  • $$3446$$ km
  • $$3464$$ km
  • $$3488$$ km
  • $$3400$$ km
An observer from the top of the light house, the angle of depression of two ships $$P$$ and $$Q$$ anchored in the sea to the same side are found to have measure $$35$$ and $$50$$ respectively. Then from the light house ...............
  • The distance of $$P$$ is more than $$Q$$.
  • The distance of $$Q$$ is more than $$P$$.
  • $$P$$ and $$Q$$ are at equal distance.
  • The relation about the distance of $$P$$ and $$Q$$ cannot be determined.
From the top of a building $$h$$ metre high, the angle of depression of an object on the ground has a measure $$\theta$$. The distance of the object from the building is
  • $$h\cos { \theta } $$ metre
  • $$h\sin { \theta } $$ metre
  • $$\tan { \theta } $$ metre
  • $$h\cot { \theta } $$
On walking ............... metres on a slope at an angle of measure 30 with the ground, one can reach the height '$$a$$' metres from the ground.
  • $$\cfrac { 2a }{ \sqrt { 3 } } $$
  • $$\cfrac { \sqrt { 3 } }{ 2 } a$$
  • $$2a$$
  • $$\cfrac{a}{2}$$
On walking $$x$$ meters, making an angle of $${30}^{o}$$ with the ground, to find a ball fallen in a valley, one can reach a depth of '$$y$$' meters below the ground, then
  • $$x=y$$
  • $$x=2y$$
  • $$2x=\sqrt { 3 } y$$
  • $$2x=y$$
When the length of the shadow of a pole is equal to the height of the pole, the angle of elevation of the Sun has measure of ................
  • $${ 30 }^{ o }$$
  • $${ 45 }^{ o }$$
  • $${ 60 }^{ o }$$
  • $${ 75 }^{ o }$$
In given figure, the minimum distance to reach from point "C" to point "A" will be ....................
626733_ab1fcfe9df564046b9f6b00d753ae88b.png
  • $$a^2$$
  • $$\sqrt 2$$
  • 2
  • 2a
An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measureWhat is the height of the tower?
  • 28.5 m
  • 30 m
  • 27 m
  • 1.5 m
The angle of elevation of a tower at a level ground is $$30^o$$ . The angle of elevation becomes $$\theta$$ when moved 10 m towards the tower. If the height of tower is $$ 5 \sqrt{3} m $$, then what is $$\theta$$ equal to ?
  • $$45^o$$
  • $$60^o$$
  • $$75^o$$
  • None of the above
What is the angle subtended by 1 m pole at a distance 1 km on the ground in sexagesimal measure ?
  • $$\frac{9} {50 \pi}$$ degree
  • $$\frac{9} {5 \pi}$$ degree
  • 3.4 minute
  • 3.5 minute
From the top of a lighthouse $$70m$$ high with its base at sea level, the angle of depression of a boat is $${ 15 }^{ o }$$. The distance of the boat from the foot of the lighthouse is:
  • $$70(2-\sqrt { 3 } )m$$
  • $$70(2+\sqrt { 3 } )m$$
  • $$70(3-\sqrt { 3 } )m$$
  • $$70(3+\sqrt { 3 } )m$$
The angles of depression of two boats as observed from the mast head of a ship $$50$$ metres high are $${45}^{o}$$ and $${30}^{o}$$. The distance between the boats, if they are on the same side of mast head in line with it, is
  • $$50\sqrt { 3 } $$ metres
  • $$0(\sqrt { 3 } +1)$$ metres
  • $$50(\sqrt { 3 } -1)$$ metres
  • $$50(1-\sqrt { 3 } )$$ metres
Two poles are 10 m and 20 m high. The line joining their tips makes an angle of $$15^o$$ with the horizontal. What is the  distance between the poles ?
  • $$10 ( \sqrt{3} - 1 ) m$$
  • $$ 5 ( 4 + 2 \sqrt{3} -1 ) m$$
  • $$20 ( \sqrt{3} + 1 ) m$$
  • $$10 ( \sqrt{3} +2 ) m$$
A person standing on the bank of a river observes that the angle subtended by a tree on the opposite of bank is $${60}^{o}$$. When he retires $$40 m$$ from the bank, he finds the angle to be $${30}^{o}$$. What is the breadth of the river?
  • $$60 m$$
  • $$40 m$$
  • $$30 m$$
  • $$20 m$$
The top of a hill observed from the top and bottom of a building of height $$h$$ is at angles of elevation $$\alpha$$ and $$\beta$$ respectively. The height of the hill is 
  • $$\cfrac { h\cot { \beta } }{ \cot { \beta } -\cot { \alpha } } $$
  • $$\cfrac { h\cot { \alpha } }{ \cot { \alpha } -\cot { \beta } } $$
  • $$\cfrac { h\tan { \alpha } }{ \tan { \alpha } -\tan { \beta } } $$
  • None of the above
A man observes two objects in a line in the west. On walking a distance $$x $$ towards the north, the objects subtends an angle $$\alpha$$ in front of him and on walking a further distance $$x$$ to north they subtend an angle, $$\beta$$, then the distance between the objects is
  • $$\cfrac { 2x }{ 2\cot { \beta } -\cot { \alpha } } $$
  • $$\cfrac { 3x }{ 2\cot { \beta } -\cot { \alpha } } $$
  • $$\cfrac { 3x }{ 2\cot { \beta } +\cot { \alpha } } $$
  • none of these
An aeroplane flying at a constant speed, parallel to the horizontal ground, $$\sqrt {3}\ km$$ above it, is observed at an elevation of $$60^{o}$$ from a point on the ground. If, after five seconds, its elevation from the same point, is $$30^{o}$$, then the speed (in $$km/ hr$$) of the aeroplane, is
  • $$1500$$
  • $$750$$
  • $$720$$
  • $$1440$$
The height of a house subtends a right angle at opposite window from the base of the house is $$60^0$$. If the width of the road be 6 metres, then the height of the house is
  • $$6 \sqrt 3 m$$
  • $$8 \sqrt 3 m$$
  • $$10 \sqrt 3 m$$
  • $$3 \sqrt 6$$
Over a tower $$AB$$ of height $$h\ mt$$, there is a flag staff $$BC, AB$$ and $$BC$$ makes equal angles at a point distant $$'d' mt$$ from the foot $$A$$ of the tower. The height of the flag staff is
  • $$\dfrac {h(d^{2} + h^{2})}{(d^{2} - h^{2})}mt$$
  • $$\dfrac {h(d^{2} - h^{2})}{(d^{2} - h^{2})}mt$$
  • $$\dfrac {h(d^{2} - h^{2})}{(d^{2} + h^{2})}mt$$
  • $$\dfrac {h(d^{2} + h^{2})}{(d^{2} + h^{2})}mt$$
The angle of elevation of the top of a tower as observed from a point on the horizontal ground is $$x$$. If we move a distance $$d$$ towards the flux of the tower, the angle of elevation increases to $$y$$, then the height of the tower is
  • $$\cfrac { d\tan { x } \tan { y } }{ \tan { y- } \tan { x } } $$
  • $$d\left( \tan { y } +\tan { x } \right) $$
  • $$d\left( \tan { y } -\tan { x } \right) $$
  • $$\cfrac { d\tan { x } \tan { y } }{ \tan { y } +\tan { x } } $$
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