Carla looks from a height of 1515 yards at the top of her apartment building. She lines up the top of a flagpole with the curb of a street 2020 yards away. If the flagpole is 1212 yards from the apartment building, how tall is the flagpole?.

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19-12-2022
Mathematics

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Carla looks from a height of 1515 yards at the top of her apartment building. She lines up the top of a flagpole with the curb of a street 2020 yards away. If the flagpole is 1212 yards from the apartment building, how tall is the flagpole?.

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-22T13:29:32-05:00

The height of the flagpole if 1212 yards away flagpole's top lines up with the curb of a street 2020 yards away when looking from a height of 1515 yards is 606 yards.

Let us represent the position Carla is as A, top of flagpole as B, curb of street as C, bottom of flagpole as D and bottom of apartment as E. Therefore, AE = 1515 yards, CE = 2020 yards and DE = 1212 yards.

Now consider ΔACE and ΔBCD,

∠ACE = ∠BCD same angle

∠CEA = ∠CDB = 90°

Therefore ΔACE is similar to ΔBCD by AA similar criterion of triangles.

In similar triangles, ratio of corresponding sides are equal. Therefore as ΔACE is similar to ΔBCD,

BD/ AE = CD/CE

BD = CD/CE × AE

BD = ( CE - DE )/CE × AE

BD = (2020 - 1212)/ 2020 × 1515

BD = 606

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