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Some Applications of Trigonometry

10th Class - CBSE - Mathematics - 2213 Questions - 0 Concepts

Important Questions

Q1 Subjective Hard
The angles of depression of the top and bottom of a building 50 meters high as 4 observed from the top of a tower are 30 and 60, respectively. Find the height of the tower and also the horizontal distance between the building and the tower. 

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Q2 Subjective Hard
From the top of a $$50\ m$$ high tower, the angles of depression of the top and bottom of a pole are observed to be $$45^{o}$$ and $$60^{o}$$ respectively. Find the height of the pole.

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Q3 Subjective Hard
Two stations due South of a leaning tower which leans towards the North, are at distances a and b from its foot. If $$\alpha$$  and $$\beta$$ are the elevations of the top of the tower from these stations, then prove that its inclination $$\theta$$ to the horizontal is given by
$$\displaystyle \cot { \theta =\frac { b\cot { \alpha  } -a\cot { \beta  }  }{ b-a }  } $$

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Q4 Subjective Hard
At a point on a level plane, a tower subtends an angle $$\alpha$$ and a man h metres high on its topp subtends an angle $$\beta$$. Prove that the height of the tower is $$\dfrac{h\tan \alpha}{\tan\beta-\tan\alpha}$$

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Q5 Subjective Hard
A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole the angle of elevation of the top of the tower is $${60^ \circ }$$ and the angle of depression of the bottom of the tower is $${30^ \circ }$$. Find the height of the pole, if the height of the tower is 75 m.

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Q6 Subjective Hard
There are two towers one on each bank of a river, just opposite to each other one tower is $$50m$$ high. From the top of this tower, the angles of depression of the top and foot of the other tower are $${30}^{o}$$ and $${60}^{o}$$ respectively. Find the width of the river and the height of the other tower.

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Q7 Subjective Hard
A flag-staff of height h stand on the top of a school building. If the angles of elevation of the and bottom of the flag-staff have measure $$\alpha$$ and $$\beta $$ are respectively from a point on the ground, prove that the height of the building is $$\dfrac { h\tan\beta  }{ \tan\alpha -\tan\beta  } $$

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Q8 Single Correct Hard
The angles of depression of two boats as observed from the mast-head of a ship $$50m$$ high are $$45^0$$ and $$30^0.$$ Tho distance between the boats, if they are on the same side of mast head in line with it, is
  • A. $$50 \sqrt{3}m$$
  • B. $$50(\sqrt{3}+1)$$m
  • C. $$5(1-\dfrac{1}{\sqrt{3}})$$m
  • D. $$50(\sqrt{3}-1)$$m

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Q9 Single Correct Hard
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
  • A. $$50\ m$$
  • B. $$43\ m$$
  • C. $$40\ m$$
  • D. $$45\ m$$

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Q10 Single Correct Hard
Which of the following statements is true?
$$I$$.  The angle of elevation of the top of a hill at the foot of the tower is $$60^o$$ and the angle of elevation of the top of the tower from the foot of the hill is $$30^o$$. If the tower is $$50\ m$$ high, then height of the hill is $$150\ m$$.
$$II$$.  An aeroplane flying horizontally $$1\ km$$ above the ground is observed at an angle $$60^o$$. After $$10\ \text{seconds}$$ its elevation changes to $$30^o$$. Then the speed of the aeroplane is $$527.04\ \text{km/h}$$.
$$III$$.  A man in a boat rowing away from light house $$100\ m$$ high takes $$2\ \text{minutes}$$ to change the angle of elevation of the top of the light house from $$60^o$$ to $$30^o$$. Then the speed of the boat is $$40\ \text{m/minute}$$.
  • A. $$II$$
  • B. $$III$$
  • C. $$I \ \&\  III$$
  • D. $$I$$

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Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65
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