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The angle of elevation from a park bench 724 feet from the base of the Gateway Arch in St. Louis, Missouri is 22°. How tall is the Gateway Arch, rounded to the nearest whole number?

Respuesta :

Answer:

Gateway Arch is [tex]292.46[/tex] feet tall

Step-by-step explanation:

As we know,

the horizontal distance from the gate of the Arch to the bench [tex]= 724[/tex] feet

The angle of elevation is [tex]22[/tex] degree

Let H be the height of the gate be "H"

Tanθ= Perpendicular/Base

Substituting the given values in above equation, we get -

[tex]tan 22 = \frac{H}{724} \\H = 724 * tan 22\\H = 724 * 0.404\\H = 292.46[/tex]feet

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