# Maths (Trigonometry)

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Raylene who was involved in an
orienteering competition. The ﬁrst two
legs of her triangular course are:
• 1.2 km on a true bearing of 200 °
• 2.3 km on a true bearing of 320 ° .
To ﬁnd the shortest way back to the
start/ﬁnish line, Raylene must
calculate the distance and bearing of
the ﬁnal leg.
1 Draw a diagram showing the ﬁrst
two legs of the course.
2 Consider the ﬁrst leg of the course.
Calculate the distance south and the
distance west of the starting point
travelled in the ﬁrst leg.
3 Now, considering only the second
leg of the course, calculate the
distance travelled north and west
during this leg.
4 Calculate how far west of the start
point Raylene is at the end of the second leg.
5 Calculate how far north or south of the start point Raylene is at the end of the
second leg.
6 Use Pythagoras’ theorem to ﬁnd the distance back to the start/ﬁnish line.
7 Find the bearing on which Raylene must run to get back to the start/ﬁnish line.
8 The organisers made an error in calculating the bearing on which to run the
second leg. It was the intention of the organisers that the ﬁnal leg of the course
be due east. Calculate the bearing on which the second leg should have been run
so that the ﬁnal leg is due east.

• Maths (Trigonometry) - ,

• Maths (Trigonometry) - ,

1 Draw a diagram showing the ﬁrst
two legs of the course.
2 Consider the ﬁrst leg of the course.
Calculate the distance south and the
distance west of the starting point
travelled in the ﬁrst leg.
3 Now, considering only the second
leg of the course, calculate the
distance travelled north and west
during this leg.
4 Calculate how far west of the start
point Raylene is at the end of the second leg.
5 Calculate how far north or south of the start point Raylene is at the end of the
second leg.
6 Use Pythagoras’ theorem to ﬁnd the distance back to the start/ﬁnish line.
7 Find the bearing on which Raylene must run to get back to the start/ﬁnish line.
8 The organisers made an error in calculating the bearing on which to run the
second leg. It was the intention of the organisers that the ﬁnal leg of the course
be due east. Calculate the bearing on which the second leg should have been run
so that the ﬁnal leg is due east.

--- These are the questions. I've done question 1 but it confuses me in question 2. Please help.

• Maths (Trigonometry) - ,

question 2. If you did this on graph paper you have the coordinates of the two points, use the distance formula.