3D trig Q (1 Viewer)

[QZP]

From 1994 HSC paper Q7:

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 26deg, 28deg, and 30deg, respectively. Determine the bearing of B from Uluru.

Any ideas? I don't know where to begin...

 

[braintic]

Call the base of Uluru O, and the height h.
You should be able to show that OA=hcot26, OB=hcot28, OC=hcot30.
The question is asking for angle AOB.
Call this angle theta, so angle BOC is 90 - theta.
Form expressions for the areas of triangles AOB, BOC and AOC, the first two involving theta [turning sin(90-theta) into cos theta]
Then form an equation based on the fact that the first two areas add to the third.
Cancel the h's, and you have an equation that you can solve using either the t-results or the auxiliary angle method.

 

[QZP]

Damn... I didn't think of considering areas. But I guess I needed to realise that all I needed was an equation with theta so I could solve for it

 

[braintic]

Damn... I didn't think of considering areas. But I guess I needed to realise that all I needed was an equation with theta so I could solve for it

Consideration of areas is useful is a number of unexpected areas. (Oh dear)
For example, deriving the perpendicular distance formula, and also the trig limits.