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

One side of a rectangular piece of paper is $$6\text{ cm}$$, the adjacent sides being longer than $$6\text{ cm}$$. One corner of the paper is folded so that it sets on the opposite longer side. If the length of the crease is $$l$$ $$\text{cm}$$ and it makes an angle $$\theta$$ with the long side as shown, then $$l$$ is
762902_85d87f11d9724e6ebe4e4d58b372c487.png
  • $$\cfrac { 3 }{ \sin ^{ 2 }{ \theta } \cos { \theta } } $$
  • $$\cfrac { 6 }{ \sin ^{ 2 }{ \theta } \cos { \theta } } $$
  • $$\cfrac { 3 }{ \sin { \theta } \cos { \theta } } $$
  • $$\cfrac { 3 }{ \sin ^{ 3 }{ \theta } } $$
The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30$$^\circ$$. If the angle of elevation at the same point is to be 45$$^\circ$$, then the pillar has to be raised to a height of how many metres?
  • 59.4 m
  • 61.4 m
  • 62.4 m
  • 63.4 m
A man on the top of a bamboo pole observes that the angle of depression of the base and the top of another pole are $${60}^{o}$$ and $${30}^{o}$$ respectively. If the second pole stands $$5$$ m above the ground level, then the height of the bamboo pole on which the man is sitting is
  • $$5$$ m
  • $$2.5$$ m
  • $$10$$ m
  • $$12.5$$ m
The angles of elevation of the top of a temple, from the foot and the top of a building $$30\ m$$ high, are $$60^{\circ}$$ and $$30^{\circ}$$ respectively. Then height of the temple is
  • $$50\ m$$
  • $$43\ m$$
  • $$40\ m$$
  • $$45\ m$$
A 25 m long ladder is placed against a vertical wall such that the foot of the ladder is 7 m from the feet of the wall. If the top of the ladder slides down by 4 cm, by how much distance will the foot of the ladder slide?
  • $$9\ m$$
  • $$15\ m$$
  • $$5\ m$$
  • $$8\ m$$
  • $$4\ m$$
The angles of elevation of the top of a tower from two points A & B lying on the horizontal through the foot of the tower are respectively $$30^{\circ}$$ and $$45^{\circ}$$ of A & B are on the same side of the tower and AB = 48 m then the height of the tower is
  • 24($$\sqrt{3} + 1)$$ m
  • 25 m
  • 26($$\sqrt{3} - 1)$$ m
  • 23 m
The angle of elevation of a tower from a point on the ground is $${30}^{o}$$. At a point on the horizontal line passing through the foot of the tower and $$100$$ meters nearer to it, the angle of elevation is found to be $${60}^{o}$$, then the height of the tower is
  • $$50\sqrt { 3 } $$ meters
  • $$\dfrac{50}{\sqrt { 3 }} $$ meters
  • $$\dfrac{100}{\sqrt { 3 } }$$ meters
  • $$100\sqrt { 3 } $$ meters
The height of a tower is $$50\sqrt {3}\ m$$. The angle of elevation of a tower from a distance $$50\ m$$ from its feet is
  • $$30^{\circ}$$
  • $$45^{\circ}$$
  • $$60^{\circ}$$
  • $$90^{\circ}$$
Choose the correct answer from the alternatives given.
A tree is broken by the wind. If the top of the tree struck the ground at an angle of $$30^\circ$$ and at a distance of 30 m from the root, then the height of the tree is
  • $$15 \sqrt 3 m$$
  • $$20 \sqrt 3 m$$
  • $$25 \sqrt 3 m$$
  • $$30 \sqrt 3 m$$
The shadow of a stick of height $$1$$ metre, when the angle of elevation of the sun is $${ 60 }^{ o }$$, will be
  • $$\cfrac { 1 }{ \sqrt { 3 } }$$ m
  • $$\cfrac { 1 }{ 3 } $$ m
  • $$\sqrt { 3 }$$ m
  • $$3$$ m
If the angle of elevation of the sun at $$8:00$$ O'clock is $$\alpha$$ and at $$10:00$$ O'clock is $$\beta$$ then ______ holds.
  • $$\alpha > \beta$$
  • $$\alpha < \beta$$
  • $$\alpha \geq \beta$$
  • $$\alpha = \beta$$
If a flag-staff of $$6m$$ height placed on the top of a tower throws a shadow of $$2\sqrt { 3 } m$$ along the ground, then what is the angle that the sun makes with the ground?
  • $${ 60 }^{ o }$$
  • $${ 45 }^{ o }\quad $$
  • $${ 30 }^{ o }$$
  • $${ 15 }^{ o }$$
The height of a chimney when it is found that on walking towards it $$100\ ft$$. in a horizontal line through its base the angular elevation of its top changes from $${30}^{o}$$ to $${45}^{o}$$ is ________
  • $$8\sqrt 3$$
  • $$50(\sqrt 3+1)$$
  • $$100(\sqrt 3+1)$$
  • None of these
The angles of depression of two points $$A$$ and $$B$$ on a horizontal plane such that $$AB = 200\ \text{m}$$ from the top $$P$$ of a tower $$PQ$$ of height $$100\ \text{m}$$ are $$45^\circ - \theta$$ and $$45^\circ + \theta$$. If the line $$AB$$ passes through $$Q$$ the foot of the tower, then angle $$\theta$$ is equal to:
  • $$45^\circ$$
  • $$30^\circ$$
  • $$22.5^\circ$$
  • $$15^\circ$$
The angle of elevation of the top of a tower from the top and bottom of a building of height $$a$$ are $$30^{\circ}$$ and $$45^{\circ}$$ respectively. If the tower and the building are at same level, the height of the tower is 
  • $$\dfrac{\sqrt{3}a(1+\sqrt{3})}{2}$$
  • $$a\left(\sqrt{3}+1\right)$$
  • $$\sqrt{3}a$$
  • $$a\left(\sqrt{3}-1\right)$$
The angle of elevation of the top of an unfinished tower at a point $$120m$$ from its base is $$45^o$$. How much higher must the tower be raised so that its angle of elevation becomes $$60^o$$ at the same point?
  • $$90m$$ 
  • $$92m$$ 
  • $$97m$$ 
  • $$87.84m$$ 
A ladder rests against a wall at an angle $$\alpha$$ to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distanced down the wall making an angle $$\beta$$ with the horizontal, then
  • $$a = b\, tan \dfrac{\alpha + \beta}{2}$$
  • $$a = b\, cot \dfrac{\alpha + \beta}{2}$$
  • $$a \, tan \dfrac{\alpha - \beta}{2}$$
  • None
The angle of elevation of the top of a tower standing on a horizontal plane from point A is $$\alpha$$. After walking a distance d towards the foot of the tower, the angle of elevation is found to be $$\beta$$. The height of the tower is
  • $$\dfrac{d \,sin\, \alpha\, sin\, \beta}{sin\, (\beta - \alpha)}$$
  • $$\dfrac{d \,sin\, (\beta - \alpha)}{sin\, \alpha\,sin\, \beta}$$
  • $$\dfrac{d \,sin\,\alpha\, sin\, \beta}{sin\, (\alpha\,- \beta)}$$
  • $$\dfrac{d\, sin\, (\alpha\, - \beta)}{sin\, \alpha\,sin \, \beta}$$
Shadow of a vertical pillar is equal to the height of the pillar then the angle of elevation of sun will be :
  • $$90^{o}$$
  • $$60^{o}$$
  • $$45^{o}$$
  • $$30^{o}$$
A vertical pole PS has two marks at Qand A such that the portions PQ, PR and PS subtend angles $$\alpha,\beta, \gamma$$ at a point on the ground distant x from the pole. If PQ = a, PR =b, PS = c and $$\alpha + \beta + \gamma$$ = 180; then $$x^{2}$$ =
  • $$\dfrac{a}{a + b + c}$$
  • $$\dfrac{b}{a + b + c}$$
  • $$\dfrac{c}{a + b + c}$$
  • $$\dfrac{abc}{a + b + c}$$
$$ABC$$ is a triangular park with $$AB = AC =100\ m$$. $$A$$ clock tower is situated at the mid-point of $$BC$$. The angles of elevation of the top of the tower at $$A$$ and $$B$$ are $$\cot^{-1} 3.2$$ and $$cosec^{-1} 2.6$$ respectively. The height of the tower is 
  • $$16\ m$$
  • $$25\ m$$
  • $$50\ m$$
  • none of these
A tower subtends an angle of $$30^o$$ at a point on the same level as the foot of the tower. At a second point h meter above the first, the depression of the foot of the tower is $$60^o$$. The horizontal distance of the tower from the point is
  • $$h\ \cot 60^o$$
  • $$\dfrac{1}{3}$$ $$h\ \cot 30^o$$
  • $$\dfrac{h}{3}$$ $$\cot 60^o$$
  • $$h\ \cot 30^o$$
A vertical tower stands on a declivity which is inclined at $$15^o$$ to the horizon. From the foot of the tower a man ascends the declivity for $$80$$ feet and then finds that the tower subtends at angle of $$30^o$$. The height of the tower is-  
  • $$20 ( \sqrt{6} - \sqrt{2})$$
  • $$40 ( \sqrt{6} - \sqrt{2})$$
  • $$40 ( \sqrt{6} + \sqrt{2})$$
  • $$none\ of\ these$$
The angle of elevation of the top of a tower at a point A on the ground is $$30$$. On walking $$20$$ metres towards the tower, the angle of elevation is $$60$$, The height of the tower 
  • $$50(\sqrt 3+1)$$
  • $$10\sqrt 3$$
  • $$8\sqrt 3$$
  • None of these
The shadow of a tower standing on a level ground is found to be $$60$$ meters longer when the suns altitude is $$30$$ than when it is $$45$$. The height, of the tower is______
  • $$30(\sqrt{3} + 1)$$
  • $$30(\sqrt{3} - 1)$$
  • $$20(\sqrt{3} + 1)$$
  • None of these

From the top of a $$25\ \text{m}$$ high pillar at the top of tower, angle of elevation is same as the angle of depression of foot of tower,  then height of tower is: 
  • $$25\ \text{m}$$
  • $$100\ \text{m}$$
  • $$75\ \text{m}$$
  • $$50\ \text{m}$$
A uniform rod is rested on a wall and its lower end is tied to the wall with the help of a horizontal string of negligible mass as shown. Length of rod is $$L$$ and height of the wall is $$h$$. What will be tension in the string? (all surface are frictionless)
1030709_e937d9fb0e554965b8e3bbecf6822c8e.png
  • $$\dfrac { mg\ell\sin { \theta } }{ 2h\cos { \theta } }$$
  • $$\dfrac { mg\ell\cos ^{ 2 }{ \theta } }{ 2h\sin { \theta } }$$
  • $$\dfrac { mg\ell\sin { \theta } \cos ^{ 2 }{ \theta } }{ 2h }$$
  • $$\dfrac { mg\ell }{ 2h\sin { \theta } \cos ^{ 2 }{ \theta } }$$
A boy playing on the roof top of a 10m high building throws a ball with a speed of 10m/s at an angle of $$30_{0}$$ with the horizontal. How far from the throwing point will the ball be at the height of 10m from the ground.
$$\sin { { 30 }^{ 0 } } =\quad \frac { 1 }{ 2 } \\ \cos { { 30 }^{ 0 } } =\quad \frac { \sqrt { 3 }  }{ 2 } $$
  • 8.66 m
  • 5.20 m
  • 4.33 m
  • 2.60 m
Find the angle of depression of a boat from the bridge at a horizontal distance of $$25$$m from the bridge, if the height of the bridge is $$25$$ m.
  • $$60^0$$
  • $$30^0$$ 
  • $$45^0$$ 
  • none
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $$20\ meters$$ high building are $${45}^{o}$$ and $${60}^{o}$$ respectively. Then the height of the tower is
  • $$20(\sqrt{3}-1)$$
  • $$20(\sqrt{3}+1)$$
  • $$\dfrac{20}{\sqrt{3}-1}$$
  • $$\dfrac{20}{\sqrt{3}+1}$$
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