CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 1 - MCQExams.com

Let $$10$$ vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $$\alpha$$ at a point $$O$$ on this line and all the poles are on the same side of $$O$$. If the height of the longest pole is $$h$$ and the distance of the foot of the smallest pole from $$O$$ is $$a$$; then the distance between two consecutive poles, is
  • $$\displaystyle \frac{h \sin \alpha + a \cos \alpha}{9 \cos \alpha}$$
  • $$\displaystyle \frac{h \cos \alpha - a \sin \alpha}{9 \sin \alpha}$$
  • $$\displaystyle \frac{h \sin \alpha + a \cos \alpha}{9 \sin \alpha}$$
  • $$\displaystyle \frac{h \cos \alpha - a \sin \alpha}{9 \cos \alpha}$$
A kite is flying at an inclination of $$60^\circ$$ with the horizontal. If the length of the thread is $$120\text{ m},$$ then the height at which kite is:
  • $$60\sqrt 3\text{ m}$$
  • $$60\text{ m}$$
  • $$\dfrac{60}{\sqrt 3}\text{ m}$$
  • $$120\text{ m}$$
A vertical pole of height $$10$$ meters stands at one corner of a rectangular field. The angle of elevation of its top from the farthest corner is $$30^{\circ}$$, while that from another corner is $$60^{\circ}$$. The area (in $$m^{2})$$ of rectangular field is
  • $$\dfrac {200\sqrt {2}}{3}$$
  • $$\dfrac {400}{\sqrt {3}}$$
  • $$\dfrac {200\sqrt {2}}{\sqrt {3}}$$
  • $$\dfrac {400\sqrt {2}}{\sqrt {3}}$$
A pole $$15$$ m long rests against a vertical wall at an angle of $$\displaystyle 30^{\circ}$$ with the ground How high up the wall does the pole reach?
  • $$5$$ m
  • $$7$$ m
  • $$7.5$$ m
  • $$8$$ m
the shadow cast by a tower is 30 m long when the elevation of sum is $$\displaystyle 30^{\circ}   $$ If the elevation of sum is $$\displaystyle 60^{\circ}   $$  then the length of the shadow is 
  • 30 m
  • 20 m
  • 10 m
  • $$\displaystyle 10\sqrt{3} m $$
The angle of depression of  a boat from the top of a cliff 300 m high is $$\displaystyle 60^{\circ}   $$  The distance of the boat from the foot of the cliff is 
  • $$\displaystyle 100 \sqrt{3} $$
  • 100
  • $$\displaystyle 300 \sqrt{3} $$
  • 300
If the length of the shadow of a pole is equal to the height , of the pole, then the angle of the elevation of the sun is 
  • $$ \displaystyle 30^{\circ} $$
  • $$ \displaystyle 75^{\circ} $$
  • $$ \displaystyle 60^{\circ} $$
  • $$ \displaystyle 45^{\circ} $$
The angle of elevation of an object viewed is the angle formed by the line of sight with the horizontal when it is
  • Above the horizontal level 
  • Below the horizontal level 
  • At the horizontal level 
  • None of the above
From the point B a perpendicular BD is drawn on AC. If $$\cos 30^o=0.8$$, find the length of AD.
374004_cd5931ba012c4846945cbdb7cb7bb2d8.png
  • $$45$$
  • $$30$$
  • $$50$$
  • $$80$$
The length of the shadow of a pole is $$\displaystyle \sqrt{3}   $$ times its height  The elevation of the sum must be 
  • $$\displaystyle 60^{\circ} $$
  • $$\displaystyle 45^{\circ} $$
  • $$\displaystyle 30^{\circ} $$
  • $$\displaystyle 15^{\circ} $$
The angle of depression of an object viewed is the angle formed by the line of sight with the horizontal when it is below the horizontal level
that is - 
  • the case when we lower our head to look at the object.
  • the case when we upper our head to look at the object.
  • the case when we look straight to the object.
  • irrelevant defination

88860_f25c34edb3c64dae8b8000055c6c355e.png
  • 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.
In the given figure given, $$\beta$$ is _____ 
452591.png
  • Angle of elevation
  • Angle of depression
  • Line of sight
  • Horizontal level
In the given figure, $$\alpha$$ is _____ 
452592_b4baa829ee724e3d99af658efd11a6f7.png
  • Angle of elevation
  • Angle of depression
  • Line of sight
  • Horizontal level
In the given figure, $$\beta$$ is _____. 
452593_324fce35104743c8970d6fcb08ad4518.png
  • Angle of elevation
  • Angle of depression
  • Line of sight
  • Horizontal level
In case of angle of elevation, the observer has to look _____ to view the object. 
  • Straight
  • Anywhere
  • Down
  • Up
From a point P on a level ground, the angle of elevation of the top tower is $$30^{\circ}$$. If the tower is $$100\ m$$ high, the distance of point P from the foot of the tower is:
  • $$149\ m$$
  • $$156\ m$$
  • $$173\ m$$
  • $$200\ m$$
The given figure represents
452590_06a58d11eba941048272c287f61ff203.png
  • Angle of elevation
  • Angle of depression
  • Right angle
  • Line of sight
In angle of elevation the observer looks ____ to view the object whereas in angle of depression he looks ____ to view object. 
  • Up, up
  • Down, down
  • Down, up
  • Up, down
If the height of a tower and the length of its shadow is equal, then the value of the angle of elevation of the sun is-
  • $$30^{\circ}$$
  • $$45^{\circ}$$
  • $$60^{\circ}$$
  • None of these
If the length of the shadow of a pole is equal to the height of the pole, then the angle of elevation of the sun is
  • $${ 30 }^{ o }\quad $$
  • $${ 75 }^{ o }$$
  • $${ 60 }^{ o }\quad $$
  • $${ 45 }^{ o }$$
The heights of two poles are $$80$$ m and $$65$$ m. If the line joining their tops makes an angle of $$45^{\circ}$$ with the horizontal, then the distance between the poles is :   
  • $$15$$ m
  • $$22.5$$ m
  • $$30$$ m
  • $$7.5$$ m
At an instant, the length of the shadow of a pole is $$\sqrt{3}$$ times the height of the pole. The angle of elevation of the sun is
  • $$30^{\circ}$$
  • $$45^{\circ}$$
  • $$60^{\circ}$$
  • $$75^{\circ}$$
Choose the correct answer from the alternative given.
A $$10$$ m long ladder is placed against a wall. It is inclined at an angle of $$30$$ to the ground. The distance (in m) of the foot of  the ladder from the wall is?
Given $$(\sqrt{3}$$ = 1.732)
  • $$7.32$$
  • $$8.26$$
  • $$8.66$$
  • $$8.16$$
If the ratio of the height of tower and the length of its shadow is $$1: \sqrt{3}$$, then the angle of elevation  of the sum has measure_________.
  • $$60$$
  • $$45$$
  • $$30$$
  • $$90$$
A $$20 m$$ pole casts a $$5 m$$ long shadow. If at the same time of the day, a building casts a shadow of $$20 m$$, how high is the building? 
  • $$400$$ m
  • $$4$$ m
  • $$80$$ m
  • $$100$$ m
A vertical post $$15$$ ft high is broken at a certain height and its upper part, not completely separated, meets the ground at an angle of $$30^{\circ}$$. Find the height at which the post is broken.
  • $$10\ ft$$
  • $$5\ ft$$
  • $$15\sqrt {3} (2 - \sqrt {3})ft$$
  • $$5\sqrt {3} ft$$
A vertical tower 50 ft. high Stands on a sloping ground. The foot of the tower is at the same level as the middle part of a vertical flag pole. From the top of the tower the angle of depression of the top and bottom of the pole are $$15^{o}$$ and $$45^{o}$$  respectively. Then the length of the pole is 100 $$\sqrt{3}$$.
  • True
  • False
A flag-staff 5 m high stands on a building 25 m high. To an observer at a height of 30 m the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is 
  • $$\dfrac{5}{2}$$
  • $$5\sqrt{\dfrac{3}{2}}$$
  • $$5\sqrt{\dfrac{2}{3}}$$
  • none of these
The angle of elevation of a certain peak when observed, from each end of a horizontal base line of length 2a is found to be $$\theta$$. When observed from the mid-point of the base the angle of elevation is $$\phi$$. Then the height of the peak is
$$\dfrac{a sin \theta sin \phi}{ \sqrt{( sin (\phi + \theta) sin ( \phi - \theta))} }$$
  • True
  • False
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