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Two observers Abu and Badu, 46 m apart, Observe on a Vertical Pole from the same side of the
bird. The angles of elevation of the bird from Abu's
and Badu's eye are 40° and 48° respectively, If at
the foot of the Pole, Abu and Badu are On the same
horizontal:
(a)illustrate the information in a diagram
(b)Calculate, Correct to One decimal place, the
height of the PO LO
​

Verified Answer :

Draw a horizontal line representing the ground.
Place two points on this line, Abu and Badu, 46 m apart.
Draw a vertical line from the point representing Abu, this is the pole.
Draw lines from Abu and Badu to the top of the pole, these lines represent their lines of sight to the bird.
The angles between the horizontal line and the lines of sight are the angles of elevation, 40° for Abu and 48° for Badu.
(b) To calculate the height of the pole, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the pole) to the adjacent side (the distance from the observer to the pole).
Let’s denote the height of the pole as h. Since Abu is at the foot of the pole, we can write the equation from Abu’s observation as:
tan
⁡
(
40
°
)
=
h
0
tan(40°)=0h​

This equation implies that the height of the pole is undefined from Abu’s perspective because he is right under the pole.
However, we can use Badu’s observation to find the height of the pole. The equation from Badu’s observation is:
tan
⁡
(
48
°
)
=
h
46
tan(48°)=46h​

Solving this equation for h gives:
h
=
46
⋅
tan
⁡
(
48
°
)
h=46⋅tan(48°)

Calculating this gives approximately 53.9 m. So, the height of the pole, correct to one decimal place, is 53.9 m.

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