Two students are using shadows to calculate the height of a pole. One says that it will be easier if they wait until the angle of the elevation to the sun is exactly 45°. Explain why the student made this suggestion.

There would be no need for fancy trigonometric calculations.
Basically, it is quite simple. How tall is the building, person, etc?
Measure the shadow.

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boffeemadrid boffeemadrid · Answer 2 · 2022-01-25T11:54:52+01:00

It is required to find why is it convenient to calculate the height of the pole when the angle of elevation of the sun is exactly [tex]45^{\circ}[/tex]

At angle of elevation [tex]45^{\circ}[/tex] the length of the shadow will be equal to the height of the pole.

For finding the height of the pole using trigonometry the tangent trigonometric ratio is used.

where

[tex]\tan\theta=\dfrac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\theta[/tex] = Angle of elevation

when [tex]\theta=45^{\circ}[/tex]

[tex]\tan45^{\circ}=1[/tex]

So, the opposite and adjacent side will have equal length.

The adjacent side here is the length of the shadow.

So, at angle of elevation [tex]45^{\circ}[/tex] the length of the shadow will be equal to the height of the pole.

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