Help with 3D Trig Problems please

[fdajkffk]

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.

 

[berkeman]

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...

 

[fdajkffk]

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.

 

[ehild]

See figure. Write the distances r and p in terms of the height of the balcony h and apply Pythagoras' Law.

ehild

 

[fdajkffk]

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

 

[Infinitum]

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!)

 

[berkeman]

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...

 

[fdajkffk]

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

 

[Infinitum]

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.

 

[fdajkffk]

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

 

[Infinitum]

I got p=3.12343...
r=2.78783...
These aren't exact values though..

How did you get that?

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..

 

[fdajkffk]

How did you get that?



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

ptan18=h rtan20=h
r/2.747=h

 

[Joffan]

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