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Archive8: These questions are taken from Board of Studies VCE 1994-97
Further Mathematics - CAT3


The following diagram is used for questions 1-3
A farmer has his house, H, 780 metres from the pier, P, and 325 meters from a swimming platform, S, as shown.  There is also a water pump on the river at W.

More Questions

VCEFM3B1.GIF (1669 bytes)

Question 1
a. 
Find the distance, in metres, of the swimming platform from the pier.
b.  Through similarity, VCE36.GIF (325 bytes), and PH:PS = 12:13, Using this result to show that the distance of the water pump from the house is 300 metres.
c.  Find the distance, in metres, of the water pump from the pier.
d.  The river runs east-west.  Find, in degrees, correct to one decimal place
i.   the angle WPH.
ii.  the bearing of the house from the pier.
Beside the river are two paddocks, PHS and FHS, with dimensions as shown
VCEFM3B2.GIF (1586 bytes)

(1997 Further Mathematics CAT3)

Question 2
a.  Find the total area of the two paddocks (correct to the nearest square metre).
b.  Find the length FH in metres (correct to one decimal place).

In another part of the farm, the farmer has a vertical communication tower at T with supporting wires anchored at Q and R and attached to a point M at the top of the tower as shown in the diagram below.  In the diagram VCE37.GIF (569 bytes) while the distance QR = 300 metres.  Assume Q, R and T are in the same horizontal plane.

VCEFM3B3.GIF (2193 bytes)

(1997 Further Mathematics CAT3)

Question 3
Find the height of the tower, h, in metres, giving your answer correct to one decimal place.
(1997 Further Mathematics CAT3)

Copyright Information:
This material is an extract of material produced by the Board of Studies, Victoria, Australia. This material is copyright and cannot be reproduced in any form without the written permission of the Board of Studies.

Visit Board of Studies Website for more information on VCE.

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