A person whose eye level is 1.5 meters above ground level looks at the top of a tree at an angle of 24^circ above the horizontal. If the tree is 20 meters away, how tall is the tree?

1 Answer
Alan P.
Jul 25, 2016

Height of tree (to nearest half meter): color(green)(10.5 " meters")

Explanation:

Assuming the situation is as indicated in the image below:enter image source here

The height of the tree is t+1.5 m

t/(20 " m") = tan(24^@)

Therefore
color(white)("XXX")"Height of tree" = 20*tan(24^@)" m" + 1.5" m"

(with the aid of a calculator)
color(white)("XXXXXXXXXXXX")~~8.905+1.5" m"

color(white)("XXXXXXXXXXXX")~~10.4 " m"

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