S Chand Class 10 CHAPTER 17 Heights and Distances Exercise 17

 Exercise 17 

Question 1

The angle of elevation of the top a tower from a point at a distance of 100m from its  a Horizontal plane is found to 60 degree. Find the height of tower

Sol: Suppose that AB = h is tower and O' is  point a horizontal plane is found that angle of elevation $60^{\circ}$

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In $\triangle O A B$

$\begin{aligned}&\tan 60^{\circ}=\frac{A B}{O A} \\&\sqrt{3}=\frac{h}{100} \\&h=100 \sqrt{3}\end{aligned}$

$=100 \times 1.732=173.2 \mathrm{~m}$

Question 2

A vertical flags staff stand on a horizontal plane . From a point distant 150m from it foot the angle of elevation of its top is found to be 30 degree find the height of the flag staff

Sol: Suppose  that $A B=h$ is a flag staff and $O$ is a point at a distance.

$150 \mathrm{~m}$ from the foot of flag staffs makes an angle $30^{\circ}$

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In  $\triangle O A B$ $\tan 30^{\circ}=\frac{A B}{O A}$

$\frac{1}{\sqrt{3}}=\frac{h}{150}$

$h=\frac{150}{\sqrt{3}}=\frac{150 \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$=\frac{150 \sqrt{3}}{3}=50 \mathrm{\sqrt{3}}=50 \times 1.732=86.6 \mathrm{~m}$

Question 3

The string of a kite is 150m and it makes an angle 60 with horizontal. find the height of the kite from the ground 

Sol:  (IMAGE TO BE ADDED)

Suppose that the height of kite h and makes an angle 

Elevation is 60 and length of string 150m 

In $\triangle O B A, \quad \sin 60^{\circ}=\frac{A B}{O A}$ =$\frac{\sqrt{3}}{2}=\frac{R}{150}$

$2 h=150 \sqrt{3}$

$h=\frac{150 \sqrt{3}}{2}=75 \mathrm {\sqrt{3}}=75 \times 1.732=129.9 \mathrm{~m}$

Question 4

If the shadow of a tower is 30 meter when the sum is 30 what is length of shadow when the sun's elevation of 60 

Sol: In first case $\theta=30^{\circ} \quad d=30 \mathrm{~m}$

Suppose that the height of tower is AB= h

$\triangle O A B$

$\begin{aligned}\operatorname{tom} 30^{0} &=\frac{h}{30} \\\frac{1}{\sqrt{3}} &=\frac{h}{30}\end{aligned}$ $\Rightarrow h=\frac{30}{\sqrt{3}}=10 \sqrt{3}$

Now second case the length of shadow is x then 

In $\triangle O A B$. $\tan 60^{\circ}=\frac{h}{x}$

$v \overline{3}=\frac{10 \sqrt{3}}{x}$

$x=\frac{10 \sqrt{3}}{\sqrt{3}}=10 \mathrm{~m}$

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Question 5