Question

The length of the shadow of the pillar is root 3 times its height. Find the angle of elevation of the source of light?

Answer 1

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf h}\put(2.8,.3){\large\bf sqrt 3h} }\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf \Theta }\end{picture}$

Let θ be the Angle of Elevation of the source of light.

tan θ =  AB / BC

⇒ tan θ =   h  

               √3 h

⇒ tan θ = 1 / √3

⇒ θ = tan⁻¹ (1 / √3)

⇒ θ = 30°

Ans:   Angle of Elevation of the source of light is 30°

Additional Information:

• tan θ is Opposite side divided by Adjacent side.
• sin θ is Opposite side divided by Hypotenuse.
• cos θ is Adjacent side divided by Hypotenuse.
• In a Right angled Triangle ABC, If one angle is 30°, then the other angle is 60° → by Angle Sum Property.
• Angle of Elevation is the angle made by the 'Line of Sight' with Horizontal when the point is above the Horizontal level.

                     

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