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A woman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 51°. she rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. how tall is the building across the street? (round to the nearest foot.)

Respuesta :

barnuts

Let us say that,

60 + x = the full length of the building across the street

x = the length of the building from three floors (60 ft)

 

We can calculate for the length of the building using the trigonometric function tan. Where tan is:

tan θ = opposite side / adjacent side

In this case, the opposite side is the length of the building starting from the woman’s ground point while the adjacent side is the length of the street.

tan 51 = (60 + x) / a                --->      a = (60 + x) / tan 51

tan 34 = x / a                           --->      a = x / tan 34

Equating the two equations:

(60 + x) / tan 51 = x / tan 34

60 + x = (tan 51 / tan 34) x

0.8308 x = 60

x = 72.22 ft

 

Therefore,

60 + x = 132.22 ft

The building across the street is around 132 ft tall.

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