Angle Of Elevation


 
 
Concept Explanation
 

Angle Of Elevation

Angle of Elevation: An angle of elevation is the angle made by the line of sight to the top of the object and the horizontal line. It is above the horizontal line i.e. the angle of elevation is made when we look up to the object. In the figure below the angle of elevation is the angle between the line of sight and the horizontal level.

 

 

Illustration: The angle of elevation of the top of a tower at the top and the foot of a pole of height 10 m are large 30^{circ} and large 60^{circ} respectively. Find the height of the tower.

SOLUTION: Let AB and CD be the pole and tower respectively.

                 Let CD = h

                Then large angle DAC=60^{circ}  and  large angle DBE=30^{circ}

Now large frac{CD}{CA}=tan;60^{circ}=sqrt{3}therefore CD=sqrt{3}CA;;;Rightarrow frac{h}{sqrt{3}}=CA

Again large frac{DE}{BE}=tan;30^{circ}=frac{1}{sqrt{3}}

large therefore (h-10)=frac{BE}{sqrt{3}}=frac{CA}{sqrt{3}}=frac{h/sqrt{3}}{sqrt{3}};;[because BE=CA]

large Rightarrow 3h-30=hRightarrow 2h=30;;;Rightarrow h=15

Hence, height of the tower = 15 m

Sample Questions
(More Questions for each concept available in Login)
Question : 1

A boy, 5 feet tall is watching a kite vertically above his head,  at a height of 200 feet from the ground. The angle of elevation of the kite from boy's eye is

Right Option : D
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Explanation
Question : 2

If a shadow of a 5-feet tall man is 5sqrt3 feet, then the elevation of the sun's altitute is

Right Option : A
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Explanation
Question : 3

The shadow of an 8 inch long pencil standing vertically on a table is 8sqrt3 inches. The angle of elevation of the top of pencil from the end point of shadow is

Right Option : B
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Explanation
 
 


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