A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

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26-10-2022
Mathematics

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A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

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YariF760999 YariF760999 · Answer 1 · 2022-10-26T04:56:28+02:00

In the given figure :

AB is height of the flagpole : AB = 25 feet

BC is the length of shadoe : BC = 42 foot

and angle FAE is the angle that the sun hits the flagpolem : FAE = θ

Since, line AE and line BC are the staright horizontal line, so they are parallel

and the line FC act as a transversal

So, Angle ACB = Angle FAE by corresponding angle properties

Now for angle ACB : line AB is opposite to the angle and the line BC is adjacent

Apply the trignometri ratio of Opposite side to adjacent side i.e. tangent of the angle

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

Substitute the value and simplify :

[tex]\begin{gathered} \tan \theta=\frac{Opposite\text{ side}}{Adjacent\text{ Side}} \\ \tan \text{ }\theta=\frac{AB}{BC} \\ \tan \theta=\frac{25}{42} \\ \tan \theta=0.5952 \\ \theta=\tan ^{-1}(0.5951) \\ \theta=30.76^o \end{gathered}[/tex]

So, angle is 30. 76 degree

Angle FAE = θ = 30.76 degree

Angle FAE = 30.76 degree

The angle that the sun hits the flagpole is 30.76 degree

Answer : The angle that the sun hits the flagpole is 30.76 degree