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°. if the smaller building is 42.5 meters tall

Sagot :

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

To learn more about height and distance visit:

brainly.com/question/15939509

#SPJ4