What is the height of the building pictured below if its shadow is 100 ft. long?

Question

01-02-2017
Mathematics

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What is the height of the building pictured below if its shadow is 100 ft. long?

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jdoe0001 jdoe0001 · Answer 1 · 2017-02-01T23:08:39+01:00

yeah.. baby, do the SOH CAH TOA with the hula hoop

[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\ % tangent tan(\theta)=\cfrac{opposite}{adjacent} [/tex]

so.. hmmm we have in the picture, an angle, and two sides,
actually, is the "adjacent" side, and the "opposite"

so.. which of those ratios give us only
the angle
the adjacent side
the opposite side?

ahhha!, is Ms tangent
so [tex]\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(42^o)=\cfrac{h}{100}[/tex]

solve for "h"