3D Trigonometry (1 Viewer)

[m0ofin]

Hello,

Several people have assured me that 3D trigonometry is in the 3u exam.

Uluru is a large rock on flat ground in Central Australia. Three tourists A, B and C are observing Uluru from the ground. A is due north of Uluru, C is due east of Uluru and B is on the line of sight from A to C and between them. The angles of elevation to the summit of Uluru from A, B and C are 26*, 28* and 30* respectively.

Determine the bearing of B from Uluru.

The answer is N4*31'E.

So far, I've drawn it and found tan26* = h/OA so OA = hcot26* where h=height and just can't get anything else.

Thanks.

 

[Hikari Clover]

回复: 3D Trigonometry

94 HSC

u got OA,OB,OC
in triangle AOC
angle OAC= inverse tan (OC/OA)

in triangle AOB
use sin rule to find angle OBA (in this case, u will get 2 angles for OBA, 1 is in 2nd quadrant,choose the bigger 1)
so bearing from O is 180-angle OAB - angle OBA

 

[m0ofin]

Re: 回复: 3D Trigonometry

Thanks for your help.

Why is angle OAC = inverse tan (OC/OA) when there is no right angle in triangle OAC? Or is there?

 

[webby234]

A is due north of O and C is due east of O, so there is a right angle between OA and OC.