How to solve this problem?

Sguyler

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Sep 3, 2013
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Can someone please explain how to solve this question as i know I need to use the Sine rule I just don't know how to apply it.

Mathematics: A cross country runner runs at 8km/h on a bearing of 150*T for 45 mins; then he changes direction to a bearing 053*E and runs 80 mins at a different speed until he is due east of the starting point.
a) How far was the second part of the run?
b) What was his speed for this section?
c) How far does he need to run to get back to the starting point?
 
Can someone please explain how to solve this question as i know I need to use the Sine rule I just don't know how to apply it.

Draw a sketch:

Mathematics: A cross country runner runs at 8km/h on a bearing of 150*T for 45 mins; Call the starting point S

then he changes direction to a bearing 053*E and runs 80 mins at a different speed Call this turning pointT

until he is due east of the starting point. Call this end point E

a) How far was the second part of the run?
b) What was his speed for this section?
c) How far does he need to run to get back to the starting point?

Using the sketch, ST = 8 * (45/60) km

and continue....

Please share your work with us .

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Start by going back and rereading the problem! You say he ran at a bearing of "150*T". I assume that is a typo but cannot figure out what it is supposed to be. "T" is not close to either "E" or "W". IF it was to be "150 W", draw a line "150 degrees West of North" (150 degrees counter-clockwise from vertical). He ran at 8 km/h for 45 min (3/4 hour) so how far did he run? Draw the line that length. "53 degrees E" is 53 degrees clock wise from vertical so at the end of the first line, draw a second line 53 degrees clockwise from the vertical. We don't know the time he ran in that direction so we don't know its length but he winds up "due east of the starting point" so draw a third line horizontally and extend both lines until they intersect. You now have a triangle in which you know two angles and the length of the side connecting those angles. That is the "ASA" congurence case. You can immediately calculate the third angle since the three angles must add to 180 degrees. Then you can use the "sine law" to find the lengths of the two other sides.
 
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