Question

From the top of a vertical pole the angle of depression to Ian standing at the foot of the pole is 43°. Liam is on the other side of the pole, and the angle of depression from the top of the pole to Liam is 52°. The boys are standing 58 m apart. Find the height of the pole, to the nearest meter

Answer 1

The height of the pole based on the angle of depression given is 62.2m.

How to calculate the height?

From the information given, Liam is on the other side of the pole, and the angle of depression from the top of the pole to Liam is 52° and the boys are standing 58 m apart.

Let the height = h

It should be noted that:

tan = opposite/adjacent

tan 43° = 58/h

tan 43° × h = 58

0.9325  × h = 58

0.9325h = 58

h = 58/0.9325

h = 62.2m

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Answer 2

The height of the pole is 26.94m

What is angle of depression?

Angle of depression is the angle between the line of sight and the horizontal.

Analysis:

let the distance from pole to the other guy be x

tan 38 = h/x

Also

tan 47 = h/58- x

(58 - x ) tan47 = xtan 38

(58 - x)(1.072) = 0.78x

62.17 - 1.072x = 0.78x

62.17 = 1.072x+0.78x

1.8x = 62.17

x = 34.54

h = xtan38

h = 34.54(0.78) = 26.94m

In conclusion, the height of pole is 26.94m

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