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A 133-foot antenna is on top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5°, while the angle of elevation to the bottom of the antenna from the same point is 21.5°. How tall is the building? (Round your answer to the nearest whole number.)

Answer :

Answer:

Explanation:

<ADC = 30.5 Degree

<BDC = 21.5 Degree

AB = 133 ft

[tex]in \Delta BCD[/tex]

[tex]tan 21.5= \frac{BC}{CD}[/tex]

[tex]CD = \frac{BC}{tan21.5}[/tex]

in[tex] \Delta ACD[/tex]

[tex]tan 30.5 =\frac{AC}{CD}[/tex]

[tex]CD = \frac{AB+BC}{tan30.5}[/tex]

[tex] \frac{BC}{tan21.5} = \frac{AB}{tan30.5} +\frac{BC}{tan30.5}[/tex]

[tex]\frac{BC}{tan21.5} - \frac{BC}{tan30.5} = 225.78[/tex]

2.5BC - 1.69BC = 225.78

BC = 281.40 ft

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