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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.

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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.

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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
$\displaystyle \cot { \theta =\frac { b\cot { \alpha } -a\cot { \beta } }{ b-a } }$

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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 $\dfrac{h\tan \alpha}{\tan\beta-\tan\alpha}$

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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.

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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.

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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 $\dfrac { h\tan\beta }{ \tan\alpha -\tan\beta }$

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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. $45\ m$

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

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. $I$

Asked in: Mathematics - Some Applications of Trigonometry

1 Verified Answer | Published on 07th 09, 2020

Questions 122475
Subjects 10
Chapters 93
Enrolled Students 65