Help with 3D Trig Problems please

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In summary, the problem involves Romeo and Paris observing Juliet's balcony at different angles of elevation. They are 100m apart and the question is to determine the height of the balcony above the ground. To solve this, you need to use basic trigonometry and Pythagoras' theorem to find the exact values of p and r in terms of h. Then, substituting those values into the equation 100^2=r^2+p^2 will give you the value of r in terms of h and a constant k. From there, you can solve for h by finding the value of k.
  • #1
fdajkffk
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From my Math Textbook
Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of 20 degrees. Paris is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of 18 degrees. Romeo and Paris are 100m apart. Determine height of balcony above the ground.

How do I solve this question?

Attempt:

I was able to find the angles of the top two triangles but I do not know where to go from there. I do not have enough information to use cosine law or sine law in order to find the height of this balcony.
 
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  • #2
fdajkffk said:
From my Math Textbook
Suppose Romeo is serenading Juliet while she is on her balcony. Romeo is facing north and sees the balcony at an angle of elevation of 20 degrees. Paris is observing the situation and is facing west. Paris sees the balcony at an angle of elevation of 18 degrees. Romeo and Paris are 100m apart. Determine height of balcony above the ground.

How do I solve this question?

Attempt:

I was able to find the angles of the top two triangles but I do not know where to go from there. I do not have enough information to use cosine law or sine law in order to find the height of this balcony.

I would start by drawing a sketch of the situation from 3 views -- [1] from overhead, with North up and East to the right, with the balcony at 0,0, [2] from the south looking north, and [3] from the east facing west. To include the fact that Romeo and Paris are 100m apart, I'd draw a circle of radius 100m on the first sketch...
 
  • #3
There's a sketch of the situation given to you in the textbook
Basically there are 2 right angle triangles. One regular triangle. The non-right triangle is 100m long. The angles given for the right angle triangles are 18 and 20. That's all that's given to you.
 
  • #4
See figure. Write the distances r and p in terms of the height of the balcony h and apply Pythagoras' Law.

ehild
 

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  • #5
http://imageshack.us/photo/my-images/837/28940098.jpg I don't have values though.
This is the sketch from the book
 
  • #6
fdajkffk said:
I don't have values though.

You need the exact values of r and p. What is p in terms of h? and r in terms of h? (Use basic trigonometry, they are right angled triangles!)
 
  • #7
fdajkffk said:
http://imageshack.us/photo/my-images/837/28940098.jpg I don't have values though.
This is the sketch from the book

You have 3 unknowns (r, p, h), and can write 3 equations. Show us your work...
 
  • #8
h/p is tan18 degrees = 0.32491...
h/r is tan20 degrees = 0.36397...
r/h is tn70degrees = 2.747...

Rearrange and sub em all together

K I'll try that
 
  • #9
fdajkffk said:
h/p is tan18 degrees = 0.32491...
h/r is tan20 degrees = 0.36397...

Sub em into each other?

Yep, so from that p = ...? r = ...?

Then use pythagoras theorem for the bottom-most triangle.
 
  • #10
I got p=3.12343...
r=2.78783...
These aren't exact values though..
How can I Pythagoras if it's not the actual length?

Answer is like 24 btw
 
  • #11
fdajkffk said:
I got p=3.12343...
r=2.78783...
These aren't exact values though..

How did you get that? :confused:

h/p is tan18 degrees = 0.32491...
h/r is tan20 degrees = 0.36397...

If you rearrange the above equations, you'd get them in terms of h..
 
  • #12
Infinitum said:
How did you get that? :confused:



If you rearrange the above equations, you'd get them in terms of h..

ptan18=h rtan20=h
r/2.747=h
 
  • #13
If you have the exact value k of p/r then you can substitute kr for p in
1002=r2+p2
to get the value of r
 

What is 3D Trigonometry?

3D Trigonometry is the branch of mathematics that deals with the measurement of sides and angles in three-dimensional figures.

How is 3D Trigonometry different from 2D Trigonometry?

In 3D Trigonometry, we work with three-dimensional figures, meaning that we have to consider the height, width, and depth of an object. In contrast, 2D Trigonometry deals with measurements in two-dimensional objects, such as triangles on a flat surface.

What are some real-life applications of 3D Trigonometry?

3D Trigonometry has various applications in fields such as engineering, architecture, and physics. For example, it can be used to calculate distances and angles in 3D space, which is crucial in designing buildings, bridges, and other structures.

What are the basic trigonometric functions in 3D Trigonometry?

The basic trigonometric functions in 3D Trigonometry are sine, cosine, and tangent. However, in 3D Trigonometry, we also have additional functions such as cotangent, cosecant, and secant that are not present in 2D Trigonometry.

How can I improve my skills in solving 3D Trigonometry problems?

To improve your skills in solving 3D Trigonometry problems, it is essential to practice regularly and familiarize yourself with the formulas and concepts. You can also seek help from tutors, online resources, and practice problems to strengthen your understanding.

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