CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 4 - MCQExams.com

A tower stands vertically on the ground. From a point on the ground which is $$25\ m$$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $$45^{\circ}$$. Then  the height $$(in\ meters)$$ of the tower is:
  • $$25 \sqrt{2}\ m$$
  • $$25 \sqrt{3}\ m$$
  • $$25\ m$$
  • $$12.5\ m$$
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground, making an angle of $$30^o$$ with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is $$10$$ m. The height of the tree is
  • $$10\left ( \sqrt{3}+1 \right )$$ m
  • $$10\sqrt{3}$$ m
  • $$10\left ( \sqrt{3}-1 \right )$$ m
  • $$\dfrac{30}{\sqrt{3}}$$ m
If the distance between the objects is $$p$$ metres, then the height $$h$$ of the tower is:
  • $$\dfrac{p\tan \alpha \tan \beta }{\tan \alpha -\tan \beta }$$
  • $$\dfrac{\tan \alpha \tan \beta }{\tan \alpha -\tan \beta }$$
  • $$\dfrac{p(\tan \alpha -\tan \beta )}{\tan \alpha \tan \beta }$$
  • none of the above
Based on the above figure, which of the following is/are correct?

88855_4098c75cccfd4051926398118bb7c62d.png
  • $$\theta _1$$ is the angle of elevation.
  • $$\theta _2$$ is the angle of depression.
  • The angle of elevation or depression is always measured from horizontal line through the point of observation.
  • $$\theta _1$$ and $$\theta _2$$ are always equal.
An aeroplane flying horizontally 1 km. above the ground is observed at an elevation of $$60^o$$ and after $$10$$ seconds the elevation is observed to be $$30^o$$. The uniform speed of the aeroplane in $$km/h$$ is
  • $$240$$
  • $$240\sqrt{3}$$
  • $$60\sqrt{3}$$
  • None of these
If the length of the shadow of a tower is $$\sqrt{3}$$ times that of its height, then the angle of elevation of the sun is
  • $$15^o$$
  • $$30^o$$
  • $$45^o$$
  • $$60^o$$
A Lamp Post, $$5\sqrt{3}m$$ high, cast a shadow $$5\ m$$ long on the ground. The suns elevation of this point is:
  • $$30^{\circ}$$
  • $$45^{\circ}$$
  • $$60^{\circ}$$
  • $$90^{\circ}$$
If the angle of depression of an object from a $$75\ m$$ high tower is $$30^o$$, then the distance of the object from the tower is
  • $$25\sqrt{3}\: m$$
  • $$50\sqrt{3}\: m$$
  • $$75\sqrt{3}\: m$$
  • $$150\ m$$
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
  • Assertion is correct, but Reason is incorrect.
  • Assertion is incorrect, but Reason is correct.
A tree breaks due to storm and the broken part bends so that the top of the tree just touches the ground, making an angle of $$30^o$$ with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is 10 m. The height of the tree is
  • $$10(\sqrt 3+1)\ m$$
  • $$10\sqrt 3\ m$$
  • $$10(\sqrt 3-1)\ m$$
  • $$\frac {10}{\sqrt 3}\ m$$
The angles of elevation of the top of a tower from two points at distance m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then the height of the tower is
  • $$\sqrt {mn}$$
  • mn
  • $$\frac {m}{n}$$
  • None of these
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 is
  • $$30^0$$
  • $$45^0$$
  • $$60^0$$
  • $$75^0$$
The length of the ladder making an angle of $$\displaystyle 45^{\circ}$$ with the ground and whose foot is $$7$$ m away from the wall is 
  • $$\displaystyle \frac{7\sqrt{2}}{2}m$$
  • $$\displaystyle 7\sqrt{2}m$$
  • $$\displaystyle 14\sqrt{2}m$$
  • $$14 m$$
A ladder is inclined to a wall making and angle of $$30^0$$ with it. A man is ascending the ladder at the rate of $$2\ \text{m/s}$$. How fast is he approaching the wall?
  • $$2\ \text{m/s}$$
  • $$1.5\ \text{m/s}$$
  • $$1\ \text{m/s}$$
  • $$0.5\ \text{m/s}$$
A tree $$6\ m$$ tall casts a $$4\ m$$ long shadow. At the same time, a flag pole casts a shadow $$50\ m$$ long. How long is the flag pole?
  • $$75\ m$$
  • $$100\ m$$
  • $$150\ m$$
  • $$50\ m$$
From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be $$\alpha $$ and $$\beta $$ where $$\alpha >\beta. $$ The height of the tower is $$130\ m,$$ $$\alpha =60^\circ$$ and $$\beta =30^\circ.$$ The distance of the extreme object from the top of the tower is ______.
  • $$65\ m$$
  • $$130\ m$$
  • $$260\ m$$
  • None of the above
The angles of elevation of an artificial satellite measured from two earth stations are $$30^0$$ and $$60^0$$ respectively. If the distance between the earth stations is 4000 km, then the height of the satellite is
  • 2000 km
  • 6000 km
  • 3464 km
  • 2828 km
The Qutub Minar casts a shadow $$150~ \text{m}$$ long, at the same time the Vikas Minar casts a shadow $$120 ~\text{m}$$ long on the ground. If the height of the Vikas Minar is $$80~ \text{m}$$, find the height of the Qutub Minar.
  • $$180~\text{m}$$
  • $$100~\text{m}$$
  • $$150~\text{m}$$
  • $$120~\text{m}$$
The distance between the tops of two trees $$20\ m$$ and $$28\ m$$ high is $$17\ m$$. The horizontal distance between the two tree is
  • $$9\ m$$
  • $$11\ m$$
  • $$15\ m$$
  • $$31\ m$$
One side of a parallelogram is 12 cm and its area is $$60 cm^2$$. If the angle between the adjacent sides is $$30^0$$, then its other side is
  • $$10$$ cm
  • $$8$$ cm
  • $$6$$ cm
  • $$4$$ cm
The angle of elevation of a tower from a point on the ground is $$30^0.$$ At a point on the horizontal line passing through the foot of the tower and $$100$$ meters nearer to it. If the angle of elevation is found to be $$60^0,$$ then height of the tower is
  • $$50\sqrt{3}$$ meters
  • $$\dfrac{50}{\sqrt{3}}$$meters
  • $$100\sqrt{3}$$meetrs
  • $$\dfrac{100}{\sqrt{3}}$$ meters
A man observes the elevation of a tower to be $$30^0.$$ After advancing 11 cm towards it, he finds that the elevation is $$45^0.$$ The height of the tower to the nearest metro is
  • 10
  • 15
  • 20
  • 22
A rope of length $$5$$ metres is tightly tied with one end at the top of a vertical pole and other end to the horizontal ground. If the rope makes an angle $$30^0$$ to the horizontal, then the height of the pole is
  • $$\dfrac{5}{2}$$m
  • $$\dfrac{5}{\sqrt{2}}$$m
  • $$5\sqrt{2}$$m
  • $$5$$ m
A round balloon of radius r subtends an angle $$\alpha$$ at the eye of the observer while the angle of elevation of its center is $$\beta$$. Then the height of the balloon is
  • $$r \cos \dfrac{\alpha}{2}\sin \beta$$
  • $$\dfrac{r \cos \alpha}{2 \sin \beta}$$
  • $$\dfrac{r \cos \alpha}{2 \cos \beta}$$
  • $$r \sin \alpha \sin \beta$$
The angle of elevation of a cloud from a point $$h$$ meters above the surface of a lake is $$300$$ and the angle of depression of its reflection is $$600$$. Then the height of the cloud above the surface of the lake is
  • $$\frac{h}{\sqrt{3}}$$
  • $$h$$
  • $$\sqrt{2}h$$
  • $$2 h$$
The shadow of a stick of height 1 meter, when the angle of elevation of the Sun is $$60^{\circ}$$, will be
  • $$\dfrac{1}{\sqrt{3}}$$ metre
  • $$\dfrac{1}{3}$$ metre
  • $$\sqrt{3}$$ metre
  • 3 metre
A man looks from the top of a vertical tower 30 metres high at a marked point upon the horizontal plane on which the tower stands. The angle of depression of this point is $$30^0.$$ The distance of the marked point from the foot of the tower is
  • $$\frac{30}{\sqrt{3}}$$m
  • $$\frac{30\sqrt{3}}{2}$$m
  • 30 m
  • $$30 \sqrt{3}$$m
Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of $$30^0$$ with the ground. If the length of the broken part is 20 metros, then the remaining part of the tree is of length
  • 20 metres
  • $$10\sqrt{3}$$ metres
  • 10 metres
  • $$10\sqrt{2}$$ metres
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 foot of the tower, the angle of elevation increases to y, then the height of the tower is
  • $$\dfrac{d tan x tan y}{tan y - tan x}$$
  • $$d (tan y + tan x)$$
  • $$d (tan y - tan x )$$
  • $$\dfrac{d tan x tan y}{tan y + tan x}$$
A man observes the elevation of a balloon to be $$30^0.$$ He then walks 1 km. towards the balloon and finds the angle of elevation now is $$60^0.$$ The height (in km) of the balloon is
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$\sqrt{3}+1$$
  • $$\sqrt{3}-1$$
  • $$\dfrac{2}{\sqrt{3}}$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 10 Maths Quiz Questions and Answers