CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 8 - MCQExams.com

From the top of the house 18 m high if the angle of elevation of the top of a tower is $$\displaystyle 45^{\circ}$$ and the angle of depression of the foot of the tower is $$\displaystyle 30^{\circ}$$, then the height of the tower is
  • $$\displaystyle 18\sqrt{3}\ \text{m}$$
  • $$\displaystyle 18(\sqrt{3}+1)\ \text{m}$$
  • $$\displaystyle 18(\sqrt{3}-1)\ \text{m}$$
  • $$\displaystyle 6\sqrt{3}\ \text{m}$$
A flagstaff of height $$\displaystyle \frac{1}{5}$$ of the height of a tower id mounted on the top of the flagstaff as seen from the ground is $$\displaystyle 45^{0}$$ and the angles of elevation of the top of a tower as seen from the same place is $$\displaystyle \theta $$, then the value of $$\displaystyle \tan \theta $$ is 
  • $$\displaystyle \frac{5}{6}$$
  • $$\displaystyle \frac{6}{5}$$
  • $$\displaystyle \frac{5\sqrt{3}}{6}$$
  • $$\displaystyle \frac{4}{5}$$
From the top of a church spire $$96$$ m high the angle of depression of two vehicles on the road at the same level as the base of the spire and on the same of it are $$\displaystyle x^{0}$$ and $$\displaystyle y^{0}$$, where $$\displaystyle \tan x^{0}$$= $$\displaystyle \frac{1}{4}$$ and $$\displaystyle y^{0}=\frac{1}{7}$$. The distance between the vehicles is
  • $$384$$ m
  • $$672$$ m
  • $$288$$ m
  • None of these
A ladder of a fire truck is elevated to an angle of $$60^{\circ}$$ and extended to a length of $$70\ feet$$. If the base of the ladder is $$7\ feet$$ above the ground, how many feet above the ground does the ladder reach? 
  • $$35\ ft$$
  • $$42\ ft$$
  • $$ 35\sqrt { 3 }\ ft$$
  • $$ 7+35\sqrt { 3 }\ ft$$
  • $$ 7+42\sqrt { 3 }\ ft$$
A kite flying at a height of 75 m from the ground is attached to a straight string  Which is inclined at an angle of $$\displaystyle 60^{\circ}$$ to the ground  The length of the string is
  • 75 m
  • $$\displaystyle 50\sqrt{3}m$$
  • 50 m
  • $$\displaystyle 75\sqrt{3}m$$
A man in a boat rowed away from a cliff $$50$$ m high It takes $$2$$ minutes to change the elevation at the top of the cliff from $$\displaystyle   60^{\circ}  $$ to $$\displaystyle   45^{\circ}  $$ The speed of the boat is 
  • $$\displaystyle \frac{9-3\sqrt{3}}{2}km/h $$
  • $$\displaystyle \frac{9+3\sqrt{2}}{2}km/h $$
  • $$\displaystyle \frac{9\sqrt{3}}{2}km/h $$
  • $$\displaystyle 9\sqrt{3}km/h $$
If the object to be viewed is below the level of the observer, then the angle by which the observer lowers his head down is called _____.
  • Angle of elevation
  • Angle of depression
  • Line of sight
  • Horizontal level
A kite is flying with the string inclined at $$\displaystyle 45^{\circ}$$ to the horizontal   If the string is straight and 50 m long the height at which the kite is flying is 
  • $$\displaystyle 25\sqrt{2}m $$
  • $$\displaystyle 50\sqrt{2}m $$
  • 25 m
  • 50 m
If the given object is above the level of the observer, then the angle by which the observer raises his head is called _____. 
  • Angle of depression
  • Angle of elevation
  • Line of sight
  • Horizontal level
The angle of elevation at the top of a tower from a point 10 m from the foot of the tower is $$\displaystyle  30^{\circ}   $$  The height of the tower is 
  • $$\displaystyle 10 \sqrt{3} $$
  • $$\displaystyle 10/ \sqrt{3} $$
  • $$\displaystyle 10 \sqrt{3}/3 $$
  • 10
An observer $$1.5$$ m tall is $$28.5$$ m away from a tower and the angle of elevation from the eye of the observer is $$45^o$$. The height of the tower is:
  • $$27$$ m
  • $$30$$ m
  • $$28.5$$ m
  • None of these
At a certain instant the ratio of the length of a pilar and its shadow are in ratio $$1:$$$$\sqrt3$$. At that instance, the angle of elevation of the sun is _____
452601_52fcd6ecedd941b299bacc65f203843f.png
  • $$30$$$$^o$$
  • $$45$$$$^o$$
  • $$60$$$$^o$$
  • $$90$$$$^o$$
A pole $$6\ \text{m}$$ high casts a shadow of $$2$$$$\sqrt 3\text{ m}$$ on the ground. At that instance, the sun's elevation is :
  • $$30$$$$^{\circ}$$
  • $$45$$$$^{\circ}$$
  • $$60$$$$^{\circ}$$
  • $$90$$$$^{\circ}$$
The height of a tower is $$100 \sqrt3$$. The angle of elevation of its top from a point $$100 m$$ away from its foot(base) is ______.
452603_351eb74f5f5b4160aefd5ee01e08e4ae.png
  • 30$$^o$$
  • 45$$^o$$
  • 60$$^o$$
  • 90$$^o$$
The string of a kite is $$100$$ m long and it makes an angle of 60$$^o$$ with the horizontal. If there is no slack in the string, the height of the kite above the ground is _____ 
452729.png
  • $$100$$$$ \sqrt3$$ m
  • $$50$$$$ \sqrt3$$ m
  • $$50$$$$ \sqrt2$$ m
  • $$100$$ m
The angle of elevation of the top of a tower from a point on the ground $$30$$ m away fro the foot of the tower is 30$$^o$$. The height of the tower is _____.
452604.png
  • $$30$$ m
  • $$10$$$$\sqrt3$$ m
  • $$10$$ m
  • $$10$$ $$\sqrt2$$ m
The angle of elevation of the top of a tower at a distance 30 m from its foot on a horizontal plane is found to be 30$$^o$$. The height of the tower is _____
  • $$17.3$$ m
  • $$57.96$$ m
  • $$17.8$$ m
  • $$173$$ m
From the top of a tower, the angle of depression of a man standing 40 m away from the tower isThen the height of the tower is:
  • 40$$\sqrt3$$ m
  • $$40$$ m
  • $$20$$ m
  • $$45$$ m
From a certain point $$100m$$ away from the foot of the tower, the angle of elevation of the top of the tower is $$60$$$$^o$$. The height of the tower is _____.
452602_9d1b448bc28841b2a76f44fa464007e5.png
  • $$50$$$$\sqrt3$$ m
  • $$100$$$$\sqrt3$$ m
  • $$\dfrac{100}{\sqrt3}$$ m
  • $$\dfrac{200}{\sqrt3}\ m$$
$$P$$ is a point on the segment joining the feet of two vertical poles of heights $$a$$ and $$b$$. The angles of elevation of the tops of the poles from $$P$$ are $$45^0$$ each. Then, the square of the distance between the tops of the poles is
  • $$\displaystyle \frac {a^2\, +\, b^2}{2}$$
  • $$a^2\, +\, b^2$$
  • $$2(a^2\, +\, b^2)$$
  • $$4(a^2\, +\, b^2)$$
A vertical pole subtends an angle $$\tan^{-1}\left (\dfrac {1}{2}\right )$$ at a point P on the ground. If the angles subtended by the upper half and the lower half of the pole at P are respectively $$\alpha$$ and $$\beta$$ then $$(\tan \alpha, \tan \beta) =$$
  • $$\left (\dfrac {1}{4}, \dfrac {1}{5}\right )$$
  • $$\left (\dfrac {1}{5}, \dfrac {2}{9}\right )$$
  • $$\left (\dfrac {2}{9}, \dfrac {1}{4}\right )$$
  • $$\left (\dfrac {1}{4}, \dfrac {2}{9}\right )$$
The horizontal distance between two towers is $$60\text{ m}$$ and the angle of depression of the top of the first tower as seen from the top of the second is $$30^o$$. If the height of the second tower be $$150\text{ m}$$, then the height of the first tower is
  • $$(150 + 60\sqrt{3}) \text{ m}$$
  • $$(150 - 60\sqrt{3}) \text{ m}$$
  • $$(150 + 20 \sqrt{3}) \text{ m}$$
  • None of these
A person observes  the top of a tower from a point $$A$$ on the ground. The elevation of the tower from this point is $$60^{\circ}$$. He moves $$60\ m$$ in the direction perpendicular to the line joining $$A$$ and base of the tower. The angle of elevation of the tower from the point is $$45^{\circ}$$. Then the height of the tower (in meters) is
  • $$60\sqrt {\displaystyle \frac{3}{2} }$$
  • $$60\sqrt {2 }$$
  • $$60\sqrt {3 }$$
  • $$60\sqrt {\displaystyle \frac{2}{3} }$$
An aeroplane leaving from Bismarck travels on a bearing of $$120^o$$, as shown in the figure. If the plane is $$295$$ miles directly east of Pierre, how far apart are Bismarck and Pierre? select your answer to the nearest mile.
478649_be646b2963744b74aefe0d1d4d2d1d62.png
  • $$170$$
  • $$160$$
  • $$150$$
  • $$140$$
In the figure, the length of $$\overline{QR}$$ is $$4$$, and $$T$$ is the midpoint of $$\overline{QS}$$. What is the length of $$\overline{RS}$$?
478583_90948594f5864032989dac885915b787.png
  • $$4$$
  • $$2\sqrt{3}$$
  • $$2\sqrt{13}$$
  • $$4\sqrt{13}$$
The angle of elevation of a stationary cloud from a point $$2500$$ m above a lake is $$15^0$$ and from the same point the angle of depression of its reflection in the lake is $$45^o$$. The height (in meters) of the cloud above the lake, given that $$\cot\,15^o=2+\sqrt{3}$$, is
  • $$2500$$
  • $$2500\sqrt{2}$$
  • $$2500\sqrt{3}$$
  • $$5000$$
An aeroplane leaving from Bismarck travels on a bearing of $$120^o$$, as shown in the figure. If the plane flew at an average rate of $$400$$ miles per hour, how many minutes (approx) had it been in the air when it was $$295$$ miles from Pierre? 
478651_4ab49cf390f44b7bbff97874c2a30b5c.png
  • $$51$$
  • $$56$$
  • $$29$$
  • $$67$$
The angle of depression of a car parked on the road from the top of a $$150 $$ m high tower is $$\displaystyle { 30 }^{ \circ  }$$. The distance of the car from the tower (in metres) is
  • $$\displaystyle 50\sqrt { 3 } $$
  • $$\displaystyle 150\sqrt { 3 } $$
  • $$\displaystyle 150\sqrt { 2 } $$
  • $$\displaystyle 75$$
A pole is $$20$$ feet high. A taut wire that is $$46$$ feet extends from the top of the pole to the ground. What is the angle of depression, to the nearest degree, from the top of the pole to the bottom of the wire?
  • $$23$$
  • $$26$$
  • $$43$$
  • $$64$$
  • $$67$$
The angles of elevation of the top of a tower from two points situated at distances $$36\ m$$ and $$64\ m$$ from its base and in the same straight line with it are complementary. What is the height of the tower?
  • $$50\ m$$
  • $$48\ m$$
  • $$25\ m$$
  • $$24\ m$$
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