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Applications to Trignometry

1.The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. 

2. The tops of two towers of height x and y standing on level ground,subtend angles of 30° and 60° respectively at the centre of the line joining their feet then find x:y.

3. From a point P on the ground the angle of elevation of the top of a tower is 30°and tht of the top of a flagstaff fixed on top of the tower is 60°. If the lenght of the flagstaff is 5m, find the height of tower.

SARAHann  Mar 10, 2017
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 #1
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Applications to Trignometry

1.The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. 

 

Let x the height of the tower

Let y the distance to the tower, if the observer moves 20m towards the tower.

 

\(\begin{array}{|rcll|} \hline \tan(45^{\circ}) = \frac{x}{y} &=& 1 \qquad & | \qquad \tan(45^{\circ}) = 1 \\ y &=& x \\\\ \tan(30^{\circ}) = \frac{x}{20+y} &=& \frac{1}{\sqrt{3}} \qquad & | \qquad \tan(30^{\circ}) = \frac{1}{\sqrt{3}} \\ \frac{x}{20+y} &=& \frac{1}{\sqrt{3}} \qquad & | \qquad y = x \\\\ \frac{x}{20+x} &=& \frac{1}{\sqrt{3}} \\ \dots \\ x &=& \frac{ 20 } { \sqrt{3} -1 } \\ \mathbf{x} & \mathbf{=} & \mathbf{27.32\ m} \\ \hline \end{array}\)

 

laugh

heureka  Mar 10, 2017
 #2
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Ty for the answer. Could ya solve the others as soon as possible?laugh

SARAHann  Mar 10, 2017

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