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12. From the top A of a building 125m above a street, the angle of elevation of the top B of a second
building on the opposite side is 18'36'and the angle of depression of the base of the second building
from A is 39° 48
(a) Calculate the width of the street​

Sagot :

Answer: 150.02 m

Step-by-step explanation:

Given

The height of building A is 125 m

the angle of elevation to the top of building B is [tex]18^{\circ}36'[/tex]

and the angle of depression of the base of Building B is [tex]39^{\circ}48'[/tex]

Suppose the width of the street is x

from the figure, we can write

[tex]\Rightarrow \tan (39^{\circ}48')=\dfrac{125}{x}\\\\\Rightarrow \tan (39.8^{\circ})=\dfrac{125}{x}\\\\\Rightarrow x=\dfrac{125}{\tan 39.8^{\circ}}\\\\\Rightarrow x=150.02\ m[/tex]

Thus, the width of the street is [tex]150.02\ m[/tex]

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