ANGLE OF ELEVATION PRACTICE PROBLEMS

Problem 1 :

Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height 10√3 m.

Solution :

BC - height of the tower

∠B = 90°

AC = hypotenuse side, BC = opposite side, AB = Adjacent side

Here we have to find θ,  known sides are opposite and adjacent. Based on this information, we have to use tan θ.

tan θ  =  Opposite side / Adjacent side

tan θ  =  BC/AB

  tan θ  =  10√3/30

  tan θ  = √3/3

  tan θ  = 1/√3

θ  =  tan^-1(1/√3)

 θ  =  tan^-1(1/√3)

θ  =  30° or π/6

Problem 2 :

A road is flanked on either side by continuous rows of houses of height 4√3 m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30° . Find the width of the road.

Solution :

AB = opposite side, BC = Adjacent side, AC = hypotenuse side

tan θ  =  Opposite side / Adjacent side

tan 30  =  AB/BC

1/√3  =  4√3/Distance from median of the road to house

BC  =  4√3(√3)  =  12

Width of the road :

=  2(BC)

=  2(12)

=  24 m

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