From the top of a building "h1" = 21m tall, the angle of elevation of the top of a taller building is β = 46°. The angle of depression of the base of the taller building is α = 39°. what is the height "h" of the taller building?
Between the viewer on the building at height "h1" = 21m and the taller building are two imagined right triangles.
The ankathete "a" of the lower triangle (α = 39 °) is the distance "a" of the two buildings. The counter-cat "h1" = 21m is the height of the observer.
Then:
a=h1tan α=21mtan 39°
a=25.933 m
The upper part of the taller building "h2" is the counter-cathedral of the upper triangle. The distance "a" is the ankathete. β = 46 °.
Then:
h2=a×tan β
h2=25.933 m×tan 46°
h2=26.854 m
h=h1+h2=21 m+26.854 m
h=47.854 m
The height of the larger building is h=47.854 m
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