Answer :
Height of taller building is 160 m
What is height and distance ?
Distance is the measurement of an object from a specific point in the horizontal direction, and height is the measurement of an object in the vertical direction.
Given that :the angle of elevation from the top of a small building to the top of a nearby taller building is 42.83°. the angle of depression to the base of the taller building is 18.33°.
Height of taller building = (x+42.5) Let the taller structure be x m taller than the shorter building.
Allow y to be the distance between them.
The elevation difference between the top of a tiny building and the top of a nearby taller building is [tex]42.83^{0}[/tex] degrees. While the angle of the depression to the bottom is[tex]18.33^{o}[/tex] degrees,Tan(42.83) = [tex]\frac{x}{y}[/tex]
y = [tex]\frac{x}{tan 42.83}[/tex].........................(1).
therefore, the angle of elevation from the base of the taller structure to the top of the smaller building is [tex]18.33^{o}[/tex] degrees, tan(18.33) =[tex]\frac{42.5}{y}[/tex]
y = [tex]\frac{42.5}{tan(18.33)}[/tex]....................(2)
from (1) & (2)
[tex]\frac{x}{tan(42.83)} =\frac{42.5}{tan (18.33)}[/tex]
[tex]x = \frac{tan ( 42.83) . 42.5}{tan (18.33)}[/tex]
x=118 m
Height of taller building = 118+42.5= 160 m
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