A flagpole casts a shadow that is 15 feet long. The angle of elevation at this time is 40°. How tall is the flagpole?

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Answer 1 · 2018-04-01T11:08:38

#color(blue)(12.59color(white)(88) "feet".#

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From the diagram you can see that we have constructed a right triangle, with height A and base 15.

Length of shadow = 15 feet.

Height of flagpole = A.

We know the angle of elevation is #40^@#. Using this angle and the tangent ratio, we can find A.

#tan(40^@)="opposite"/"adjacent"=A/15#

#:.#

#tan(40^@)=A/15#

Rearranging:

#A=15tan(40^@)#

By calculator:

#A=color(blue)(12.59)# feet. ( 2 d.p.)