Maths help, URGENT!!!! (1 Viewer)

[Farhanthestudent005]

A tower is built on flat ground. Three tourists A,B and C are observing the tower from ground level. A is due north of the tower, C is due east and B is on the line of sight from A and C and between them. The angles of elevation to the top of the tower rom A,B and C are 26 degrees, 28 degrees and 30 degrees respectively. What is the bearing of B from the tower??

 

[jimmysmith560]

This question has been worded differently but has retained the same important information throughout the years. Here's a solution:



I hope this helps!

 

[Eagle Mum]

@jimmysmith560, I think it’s a more complex 3D problem??
Is ‘O‘ the bottom or top of the tower?

 

[Farhanthestudent005]

Thanks for your help mate

 

[jimmysmith560]

@jimmysmith560, I think it’s a more complex 3D problem??
Is ‘O‘ the bottom or top of the tower?

I'm not entirely sure, since this is not my own solution.

Thanks for your help mate

No worries. Did that help?

 

[Farhanthestudent005]

Yes my friend

 

[CM_Tutor]

@jimmysmith560, I think it’s a more complex 3D problem??
Is ‘O‘ the bottom or top of the tower?

Yes, with 'O' the base of the tower and its height being h, then



and similarly for OB and OC and then work in the base triangle OAC making sure to find the solution with B between A and C.

This is a variation on the (IIRC) 1993 3u HSC question 7(b) about Uluru

Addendum:
Actually, it's a straight steal of the 1994 3u HSC q 7(b):

"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^o , 28^o and 30^o , respectively. Determine the bearing of B from Uluru. "

 

[jimmysmith560]

Yes, with 'O' the base of the tower and its height being h, then



and similarly for OB and OC and then work in the base triangle OAC making sure to find the solution with B between A and C.

This is a variation on the (IIRC) 1993 3u HSC question 7(b) about Uluru

Addendum:
Actually, it's a straight steal of the 1994 3u HSC q 7(b):

"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^o , 28^o and 30^o , respectively. Determine the bearing of B from Uluru. "

Yep!

There have been several variations of this question that have retained the same values. The Uluru variant was posted on BoS in 2007. There's also a Paris/Eiffel Tower variant:

"The Eiffel Tower is located in Paris, a city built on a flat floodplain. Three tourists A, B and C are observing the Eiffel Tower from the ground. A is due north of the tower, C is due east of the tower, and B is on the line-of-sight from A to C and between them. The angles of elevation to the top of the Eiffel Tower from A, B and C are 26°, 28° and 30°, respectively. Determine the bearing of B from the Eiffel Tower."

Fascinating stuff.

 

[CM_Tutor]

I'm sure there are plenty of variations, they were popular after the '94 HSC and reappear from time to time. Always a good reminder of the sine rule giving two angle solutions and the importance of considering if only one or both are valid in a given circumstance.

 

[tickboom]

A bit late to the game but I recently gave a variant of this question to my top year 9 class. Understandably they struggled and requested an explanation, so posting here in case it helps any future students: