3D trig (1 Viewer)

[Trebla]

From three collinear points, A, B, and C on the ground, the angles of elevation of the top of a mast are 30 degrees, 45 degrees and 60 degrees respectively. if AB = 90m and BC = 150m, find the exact height of the mast.

I keep getting undefined answers with my methods. Please help.

 

[KFunk]

From three collinear points, A, B, and C on the ground, the angles of elevation of the top of a mast are 30 degrees, 45 degrees and 60 degrees respectively. if AB = 90m and BC = 150m, find the exact height of the mast.

I keep getting undefined answers with my methods. Please help.

Let the top of the mast be H and the point vertically below it be D.


In ΔABH we have sin30°/BH = sin15°/90 ---> BH = 90sin30°/sin15°

In Δ BDH (right angled) we have sin45° = h/BH ---> BH = h/sin45° where h is the height of the mast.

combining both we have: h = 90sin30°sin45°/sin15°

 

[Trebla]

In ΔABH we have sin30°/BH = sin15°/90 ---> BH = 90sin30°/sin15°

I don't understand how you got this bit and how you got sin 15.

 

[香港!]

I don't understand how you got this bit and how you got sin 15.

I haven't read or tried to do the question, but that looks like it comes from the sin rule?
(sinA)\a=(sinB)\b

 

[Trebla]

Um.. help?

 

[Trev]

Since angle DBH is 45, then angle ABH would be 135, angle AHB is 180 - (30 + 135).
If you look at the diagram you can figure it out...

 

[Trev]

I did this:
tan30° = 1/√3 = h/(240+x) [1]
tan45° = 1 = h/(x+150) [2]
tan60° = √3 = h/x [3]

Combining [1] and [3] gives:
(240+x)/√3 = x√3
240+x=3x
x=120

Using [2]
h = 250+120 = 270m

 

[brett86]

 

[Trebla]

What The Hell!!! Why Has Everyone Got Different Answers Yet With Reasonable Methods???!!!!!

 

[KFunk]

Because I made the invalid assumption that A, B and C are in line with the mast . Go with brett's method, it's solid.

 

[Trev]

I had my diagram like this:
|
|
|--- C --- B --- A
ie. the co-linear points are perp. to the mast.

 

[Trebla]

So is it a 2D or 3D question? Both of them end up with different answers.

 

[acmilan]

Depends on interpretation. Seeing as how its a 3 unit question, it most likely is a 3D question.