The top of a 200m tall building, the angle elevation to the top another building 40°. The angle depression the bottom of the 2nd building?

Question

From the top of a 200m tall office building, the angle of elevation to the top of another building is 40°. The angle of depression to the bottom of the second building is 25°. How tall is the second building. plz give me answer fast

Answer 1

Draw the figure of the two buildings on a piece of paper.

AB is the building of height 200 m with point B on the ground.

DC is the other building with point C on the ground.

Draw a horizontal line from A meeting DC at point E. Now, EC = AB = 200.

Draw line segments AD and AC.



Then:

Angle EAD = elevation angle = 40 degrees. And tan(40 degrees) = DE/EA => EA = DE/tan(40 deg)

Angle EAC = depression angle = 25 degrees. And tan(25 degrees) = EC/EA => EA = EC/tan(25 deg)



Since EA is the same (it s the distance between the two buildings), we have:



DE/tan(40 deg) = EC/tan(25 deg)

DE/tan(40 deg) = 200/tan(25 deg)

DE = [ 200/tan(25 deg) ] * tan(40 deg)

DE = 359.9



Height of second building is DC.

DC = DE + EC = 359.9 + 200 = 559.9



Answer: Height of second building is 559.9 meters.

Answer 2

The second building is 559.890993211 meters tall, or approximately 559.89 meters tall. While solving this problem, an assumption was made that the bases of both building were level. Now, onto the solving process.



Firstly, draw a diagram with two parallel and vertical line segments representing the first building (known as Building A from now on) and and the taller second building (known as Building B from now on) aligned on one end (the "ground").



Draw a horizontal line segment, preferably dashed for easy illustration, perpendicular from the top of the first building to the second building and label it "a" (the letter is unimportant).



This line splits Building B into two segments. Label the top segment "o" (again, the letter is unimportant).



Label the entire line segment of Building B "x". We're solving for x.



We know that Building A is 200 m tall, so write "200 m" next to that segment and the bottom segment of Building B. Since there is a perpendicular line from the top of the line segment representing Building A that splits the parallel segment representing Building B, we know that the bottom segment of Building B is the same height as Building A.



Label, the angle formed by a and the line segment from the top of Building A to the top of Building B with 40°, as that is that angle of elevation. Label the angle formed by a and the line segment from the top of Building A to the base of Building B with 25° as that is that angle of depression.



Now, if we find the length of a, we can find the length of o and add that to 200 m to find the height of Building B.



To find the length of a, we can use the length of of the bottom segment of Building B (200 m) in the triangle it is a part of (the bottom triangle in the diagram you drew).



tan (25°)=opposite/adjacent=200/a

a=200/tan (25°)

a≈200/0.46630765815≈428.901384102 m



Now that we know the length of a, we can find the length of o.



tan (40°)=opposite/adjacent=o/a≈o/428.901384102

o≈tan (40°)*428.901384102

o≈559.890993211 m



Finally, to find the height of Building B (the second building), x, we need to add o to the height of the bottom segment of Building B (200 m):



o+200≈559.890993211+200≈759.890993211≈759.89



Therefore, the second building is approximately 759.89 meters tall.



P.S.: I also added a picture of a diagram to this answer. Hopefully, it shows up.

Answer 3

h1 = height of first building = 200 m

h2 = height of second building = to be determined

Δh = difference between building heights = to be determined

α = angle of elevation to top of second building = 40 °

β = angle of depression to bottom of second building = 25 °

θ = angle between side of first building and line of sight

to the bottom of second building = to be determined

d = distance between the first and second buildings = to be determined



Consider a triangle starting at the top of the first building (point A), extending along

the line of sight to the bottom of the second building (Point B) and horizontally to

the bottom of the first building (Point C). The angle between Line AB and Line AC

is Angle θ.



θ = 90° - β

θ = 90° - 25°

θ = 65 °



Since we already know the height of the first building, we can now figure the

horizontal distance between the first building and the second building.



tan θ = d / h1

h1(tan θ) = d

d = h1(tan θ)

d = (200 m)(tan 65°)

d = 428.9 m



We can now calculate the difference between the height of the first building and

the height of the second building.



tan α = Δh / d

d(tan α) = Δh

Δh = d(tan α)

Δh = (428.9 m)(tan 40°)

Δh = 359.9 m



Since…



Δh = h2 - h1



then…



h1 + Δh = h2

h2 = h1 + Δh

h2 = 200 m + 359.9m

h2 = 559.9 m = 560 m Height of 2nd Building