Cambridge International Mathematics

Trigonometry (Chapter 15) 321

4 Find the unknowns correct to 3 significant figures:

abc

de f

gh i

5 Findμusing trigonometry in the following. What conclusions can you draw?

abc

Discovery 2 Hipparchus and the universe

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Hipparchuswas a Greek astronomer and mathematician born in Nicaea in the 2 nd century BC. He is

considered among the greatest astronomers of antiquity.

Part 1: How Hipparchus measured the distance to the moon

Consider two towns A and B on the earth’s equator. The

moon is directly overhead town A. From B the moon is

just visible, since MB is a tangent to the earth and is

therefore perpendicular to BC. Angle C is the difference

in longitude between towns A and B, which Hipparchus

calculated to be approximately 89 oin the 2 nd century BC.

We know today that the radius of the earth is

approximately 6378 km. Hipparchus would have used

a less accurate figure, probably based on Eratosthenes’

measure of the earth’s circumference.

5m

32°

xm

6cm

q

8cm

12 cm

xcm

50°

xm

7m

31°

q

4cm

6cm

q

f

42°

xm

ym

11 m

15 cm

xcm

10 cm

8cm

q

20 m

39°

12 m

xm

q

9cm

7cm

q

xcm

8.1 m

7.9 m

q

14 mm

12 mm

q 8.6 km

8.6 km

q

M

Moon

B

A C

Earth

r

r

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Y:\HAESE\IGCSE01\IG01_15\321IGCSE01_15.CDR Tuesday, 7 October 2008 2:05:57 PM PETER