CBSE Questions for Class 10 Maths Some Applications Of Trigonometry Quiz 13 - MCQExams.com

From the top of a cliff  $$24\mathrm { mt }$$  height, a man observes the angle of depression of a boat is to be  $$60 ^ { \circ } .$$  The distance of the boat from the foot of the cliff is
  • $$8 \sqrt { 3 } \mathrm { mt }$$
  • $$8 \sqrt { 2 } \mathrm { mt }$$
  • $$8 \sqrt { 5 } \mathrm { mt }$$
  • $$8 \mathrm { mt }$$
If the angle of elevation of a cloud from a point P which is $$25$$ m above a lake be $$30^0$$ and the angle of depression of reflection of the cloud in the lake from P be $$60^0$$, then the height of the cloud (in meters) from the surface of the lake is:
  • $$42$$
  • $$50$$
  • $$45$$
  • $$60$$

A tower of height $$'h'$$ standing vertically at the center of a square f side length $$'a'$$ subtends the same angle $$'\theta '$$ at all the corner points of the square. Then
  • $$2h^{2} = a^{2} tan^{2} \theta$$
  • $$a^{2} = 2h^{2}tan^{2} \theta$$
  • $$a^{2} = 2h^{2}cot^{2} \theta$$
  • $$2a^{2} = h^{2}cot^{2} \theta$$
The angle of elevation of the top of a tower at a distance of 30 m from its foot is $$60^\circ$$. The height of the tower is
  • $$20$$m
  • $$30\sqrt{3}$$m
  • $$15\sqrt{2}$$m
  • $$\cfrac{15}{\sqrt{2}}$$m
If a pole  $$12\ { m }$$  high casts a shadow  $$4\sqrt { 3 }\ { m }$$  long on the ground then the angle of elevation is
  • $$30 ^ { \circ }$$
  • $$45 ^ { \circ }$$
  • $$60 ^ { \circ }$$
  • $$90 ^ { \circ }$$
The shadow of a tower of height $$(1+\sqrt { 3 } )$$ m standing on the ground is found to be 2 m longer when the sun's elevation is $$30^0$$, then when the sun's elevation was
  •  $$30^0$$
  •  $$45^0$$
  •  $$60^0$$
  •  $$75^0$$
A man is standing on the deck of a ship, which is $$10\ m$$ above water level. He observes the angle of elevation of the top of a light house as $$60^0$$ and the angle of depression of the base of lighthouse as $$30^0$$. Find the height of the light house.
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  • $$40\ m$$
  • $$50\ m$$
  • $$60\ m$$
  • $$30\ m$$
A ladder $$9m$$ long reaches a point $$9m$$ below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is $$60^0$$. What is the height of the flagstaff ? 
  • $$9$$ m
  • $$10.5$$ m
  • $$13.5$$ m
  • $$15$$ m
The tops of two poles of height $$18$$m and $$10$$m are connected by wire. If the wire makes an angle of measure $$45^o$$ with the horizontal, then the length of wire is _________.
  • $$16$$m
  • $$18$$m
  • $$8\sqrt{2}$$m
  • $$8$$m
From two points A and B on the same side of a building the angles of elevation of the top of the building is $$\displaystyle 30^{\circ}$$ and $$\displaystyle 60^{\circ}$$ respectively. If height of the building is 10 m, find the distance between A and B correct to two decimal places 
  • 10.66 m
  • 13.43 m
  • 11.55 m
  • 12.26 m
The top of a broken tree touches the ground at a distance of $$12 \,m$$ from its base. If the tree is broken at a height of $$5 \,m$$ from the ground hen the actual height of the tree is
  • $$25 \,m$$
  • $$13 \,m$$
  • $$18 \,m$$
  • $$17 \,m$$
The ratio of the length of a tree and its shadow is $$ 1: 
\frac{1}{\sqrt{3}} $$. The angle of the sun's elevation is
  • $$ 30^o $$
  • $$ 45^o $$
  • $$ 60^o $$
  • $$ 90^o $$
Find the angle of elevation of the top of a tower, whose height is $$ 100 m$$, at a point whose distance from the base of the tower is $$ 100 m$$.
  • $$ 30^o $$
  • $$ 60^o $$
  • $$ 45^o $$
  • $$ 90^o $$
Choose the correct alternative answer for the following question.
When we see at a higher level, from the horizontal line, angle formed is .............
  • angle of elevation
  • angle of depression
  • 0
  • straight angle
If the shadow of 10 m high tree is $$ 10 \sqrt{3} \ m $$, then find the angle of elevation of the sun.
  • $$ 60^o $$
  • $$ 90^o $$
  • $$ 45^o $$
  • $$ 30^o $$
The shadow length of a vertical pillar is same as the height of pillar, then angle of elevation of sun is___.
  • $$45^{\circ}$$
  • $$30^{\circ}$$
  • $$60^{\circ}$$
  • $$50^{\circ}$$
If ratio of length of a vertical rod and length of its shadow is $$1 : \sqrt{3}$$, then angle of elevation of sun is :
  • $$30^{0}$$
  • $$45^{0}$$
  • $$60^{0}$$
  • $$90^{0}$$
If angle of elevation of sum is $$45^{0}$$ then the length of the shadow casts by a $$12 m$$ high tree is
  • $$6\sqrt{3}m$$
  • $$12\sqrt{3}m$$
  • $$\frac{12}{\sqrt{3}}m$$
  • $$12m$$
A kite is flying at a height of $$30 m$$ from the ground. The length of string from the kite to the ground is $$60 m$$. Assuming that there is no slack in the string, the angle of elevation of the kite at the
ground is :
  • $$45^{0}$$
  • $$30^{0}$$
  • $$60^{0}$$
  • $$90^{0}$$
If the angle of elevation of a point at the horizontal slope of a hill is $$60^{0}$$. If one has to walk $$300 m$$ to reach the top of the hill from the point then the distance of the point from the foot of the hill is:
  • $$300\sqrt{3}m$$
  • $$150m$$
  • $$150\sqrt{3}m$$
  • $$\frac{150}{\sqrt{3}}m$$
If the height of a pole is $$6 m$$ and the length of its shadow is $$2\sqrt{3} m$$, then the angle of elevation of sun is equal to
  • $$60^{0}$$
  • $$45^{0}$$
  • $$30^{0}$$
  • $$90^{0}$$
A $$25\ m$$ ladder is placed against a vertical wall of a building. The foot of the ladder is $$7\ m$$ from the base of the building. If the top of the ladder slips $$4\ m$$, then the foot of the ladder will slide by:
  • $$5\ m$$
  • $$8\ m$$
  • $$9\ m$$
  • $$15\ m$$
From the top of cliff $$300\ meters$$ high, the top of tower was observed at an angle of depression $${30}^{\circ}$$ and from the foot of the tower the top of the cliff was observed at an angle of elevation $${45}^{\circ}$$. The height of the tower is
  • $$50\left( 3-\sqrt { 3 }  \right) m$$
  • $$200\left( 3-\sqrt { 3 }  \right) m$$
  • $$100\left( 3-\sqrt { 3 }  \right) m$$
  • $$None\ of\ these$$
From the top of a tree on one side of a street the angles of elevation and depression of the top and foot of a tower on the opposite side are respectively found to be $$\alpha$$ and $$\beta$$. If $$h$$ is the height of the tree, then the height of the tower is:
  • $$\displaystyle \frac{h\sin(\alpha+\beta)}{\cos\alpha\sin\beta}$$
  • $$\displaystyle \frac{h\sin(\alpha+\beta)}{\sin\alpha\cos\beta}$$
  • $$\displaystyle \frac{h\cos(\alpha-\beta)}{\cos\alpha\cos\beta}$$
  • $$\displaystyle \frac{h\cos(\alpha+\beta)}{\cos\alpha\cos\beta}$$
A lamp post standing at a point $$A$$ on a circular path of radius $$r$$ subtends an angle $$\alpha$$ at some point $$B$$ on the path, and $$AB$$ subtends an angle of $$45^{\circ}$$ at any other point on the path, the height of the lamp post is
  • $$\sqrt{2}r\cot\alpha$$
  • $$\displaystyle \frac{r}{\sqrt{2}}\tan\alpha$$
  • $$\sqrt{2}r\tan\alpha$$
  • $$\displaystyle \frac{r}{\sqrt{2}}\cot\alpha$$
A tower subtends an angle $$\alpha$$ at a point on the same level as the root of the tower and at a second point, $$b$$ meters above the first, the angle of depression of the foot of the tower is $$\beta$$. The height of the tower is
  • $$b\cot { \alpha  } \tan { \beta  } $$
  • $$b\tan { \alpha  } \tan { \beta  } $$
  • $$b\tan { \alpha  } \cot { \beta  } $$
  • None of these
A person walking along a canal observes that two objects are in the same line which is inclined at an angle $$\alpha$$ to the canal. He walks a distance $$C$$ for the and observes that the objects subtended their greatest angle $$\beta$$ then the distance between the object is
  • $$\displaystyle \frac{2C\sin\alpha\sin\beta}{\cos\beta-\cos\alpha}$$
  • $$\displaystyle \frac{2C\sin\alpha\sin\beta}{\cos\alpha-\cos\beta}$$
  • $$\displaystyle \frac{2C\sin\alpha\sin\beta}{\cos\alpha+\cos\beta}$$
  • $$\displaystyle \frac{2C\cos\alpha\cos\beta}{\sin\alpha-\sin\beta}$$
The angular depression of the top and the foot of a tower as seen from the top of a second tower which is $$150m$$ high and standing on the same level as the first are $$\alpha$$ and $$\beta$$ respectively. If $$\tan\alpha=\dfrac{4}{3}$$ and $$\tan\beta=\dfrac{5}{2}$$, the distance between their tops is:
  • $$100m$$
  • $$120m$$
  • $$110m$$
  • $$130m$$
Vertical pole $$PO$$ stands at the centre $$O$$ of a square $$ABCD$$. If $$AC$$ subtends an angle at the top $$P$$ of the pole, then the angle $$90^{0}$$ subtended by a side of the square at $$p$$ is
  • $$30^{0}$$
  • $$45^{0}$$
  • $$60^{0}$$
  • $$90^{0}$$
At the foot of a mountain the elevation of its peak is found to be $$\displaystyle \frac{\pi }{4}.$$ After ascending $$ h $$ metres toward the mountain up a slope of $$\displaystyle \frac{\pi }{6}$$ inclination, the elevation is found to be $$\displaystyle \frac{\pi }{3}.$$ Height of the mountain is
  • $$\displaystyle \frac{h}{2}(\sqrt{3}+1)m$$
  • $$h(\sqrt{3}+1)m$$
  • $$\displaystyle \frac{h}{2}(\sqrt{3}-1)m$$
  • $$h(\sqrt{3}-1)m$$
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