Kelongs (SPM Additional Mathematics 2019)

Solution by scale drawing is not accepted.
Diagram 3 shows the positions of jetty OO and kelongs KK, LL, RR, SS, and TT in the sea. Kelong LL is situated 400m400 \mathrm{m} from jetty OO and kelong RR is situated 600m600 \mathrm{m} from jetty OO in the direction of OLOL. Kelong SS is situated 300m300 \mathrm{m} from jetty OO and kelong TT is situated 600m600 \mathrm{m} from kelong SS in the direction of OSOS. Kelongs LL, KK, and TT are situated on a straight line such that the distance of kelong KK from kelong TT is 55 times its distance from kelong LL.

If Joe uses a pair of binoculars to observe kelong RR from kelong SS, determine whether kelong RR can be seen without being blocked by kelong KK or otherwise.
Prove your answer mathematically.

I tried to answer this question by using vectors and deciding whether the vectors SK\overrightarrow{SK} and KR\overrightarrow{KR} are collinear with vector SR\overrightarrow{SR} or not. From my calculations, it seems that the answer should be that kelong RR can be seen from kelong SS without being blocked by kelong KK, but I'm not sure whether my answer is right or wrong.

Note by Tan Chin Cheern
1 year, 7 months ago

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Menelaus’s Theorem will give you the answer. K would block the view if distance of kelong K from kelong T was 3 times its distance from kelong LL instead of 5 times.

Maria Kozlowska - 1 year, 7 months ago

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