Angle of Elevation and Depression

In summary, the man standing on a 48.5m building is looking at a second building with an angle of depression of 50 degrees at the top and 80 degrees at the foot. The height from the foot to the eye of the man is 1.5m. To find the height of the second building, the formula for tan is used twice, eliminating the distance between the buildings and solving for the difference in height. The result is found to be h, the height of the second building.
  • #1
hiineko
63
1
A man is standing on a 48.5 building and is looking on a second building. The angle of depression of the top and foot of the second building is 50 degrees and 80 degrees, respectively. What is the height of the second building? The height from the foot to the eye of the man is 1.5 m.

Hello guys!
I tried answering this problem and I kind of a lost of what to do here. This is my illustration, I don't know if I drew the correct illustration. Any help for answering this hard question (for me lol) will be appreciated. Thank you and God bless!
hKtFkD0.png
 
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  • #2
What have you tried till now ?
 
  • #3
Qwertywerty said:
What have you tried till now ?

First I tried getting it using soh cah toa which I got really lost because I don't know how will I apply soh cah toa here.
I have the angle but I don't know how to use the 48.5 and 1.5.
 
  • #4
hiineko said:
First I tried getting it using soh cah toa which I got really lost because I don't know how will I apply soh cah toa here.

What is ' soh cah toa ' ?
 
  • #5
Qwertywerty said:
What is ' soh cah toa ' ?
Uhhh like this?

Ov8AoyO.png
 
  • #6
Take distance between the two buildings as , say , d .

Write the formula for tan twice . Eliminate d . Solve .

Qwertywerty said:
What is ' soh cah toa ' ?
hiineko said:
Uhhh like this?

I haven't heard of that before .
 
  • #7
Qwertywerty said:
Take distance between the two buildings as , say , d .

Write the formula for tan twice . Eliminate d . Solve .

I haven't heard of that before .

Okay sir can you be a little specific, I'm getting into it. How do I take the distance between the two buildings sir?
 
  • #8
There is some unknown distance between the buildings . Let this be a variable d , or any other of your liking .

Let difference in height of buildings be h .
Now write tan from the top of the second building . Then from the bottom .

Thus find h .
 
  • #9
Qwertywerty said:
There is some unknown distance between the buildings . Let this be a variable d , or any other of your liking .

Let difference in height of buildings be h .
Now write tan from the top of the second building . Then from the bottom .

Thus find h .
Okay will update you later sir. Thankyou for the help! Hoping I can get it this time.
 
  • #10
Qwertywerty said:
There is some unknown distance between the buildings . Let this be a variable d , or any other of your liking .

Let difference in height of buildings be h .
Now write tan from the top of the second building . Then from the bottom .

Thus find h .

Got it sir! (pls excuse my bad hand writing lol) Thankyou for assisting me. Cheers mate
wV02VIR.png
 
  • Like
Likes Qwertywerty

Related to Angle of Elevation and Depression

1. What is the difference between angle of elevation and angle of depression?

Angle of elevation and angle of depression are both measurements used in trigonometry to describe the position of an object in relation to the observer. The main difference between the two is that angle of elevation is measured upwards from the horizontal line, while angle of depression is measured downwards from the horizontal line.

2. How do you calculate the angle of elevation or depression?

The angle of elevation or depression can be calculated using the tangent function, which is the ratio of the opposite side to the adjacent side of a right triangle. To find the angle, you would use the inverse tangent function (arctan) on a scientific calculator or manually solve for the angle using the given sides of the triangle.

3. What are some real-life applications of angle of elevation and depression?

Angle of elevation and depression are commonly used in navigation, surveying, and engineering. For example, in navigation, pilots and sailors use the angle of elevation to determine the height of objects such as mountains or buildings, while surveyors use it to measure the height of structures. In engineering, these angles are used to determine the slope and elevation of roads and buildings.

4. How does the angle of elevation or depression affect the distance to an object?

The angle of elevation or depression does not directly affect the distance to an object. However, it can be used in conjunction with the distance and height of an object to calculate the horizontal distance between the object and the observer. This is commonly used in surveying and navigation to determine the location of an object or point.

5. Can the angle of elevation or depression be negative?

Yes, the angle of elevation or depression can be negative. This occurs when the object is below the horizontal line (for angle of elevation) or when the object is above the horizontal line (for angle of depression). When using trigonometric functions, negative angles are represented by a negative sign in front of the angle measurement (e.g. -30 degrees).

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