322 Trigonometry (Chapter 15)1 User= 6378km and BCMb =89oto estimate the distance from the centre of the earth C to the
moon.2 Now calculate the distance AMbetweenthe earth and the moon.3 In calculating just one distance between the earth and the moon, Hipparchus was assuming that the
orbit of the moon was circular. In fact it is not. Research the shortest and greatest distances to the
moon. How were these distances determined? How do they compare with Hipparchus’ method?Part 2: How Hipparchus measured the radius of the moon
From town A on the earth’s surface, the
angle between an imaginary line to the
centre of the moon and an imaginary line
to the edge of the moon (a tangent to the
moon) is about 0 : 25 o:
The average distance from the earth to
the moon is about384 403km.1 Confirm from the diagram that sin 0 : 25 o=
r
r+ 384 403:
2 Solve this equation to findr, the radius of the moon.3 Research the actual radius of the moon, and if possible find out how it was calculated.
How does your answer to 2 compare?The trigonometric ratios can be used to solve a wide variety of problems involving right angled triangles.
When solving such problems it is important to follow the steps below:Step 1: Read the question carefully.
Step 2: Draw a diagram, not necessarily to scale, with the given information clearly marked.
Step 3: If necessary, label the vertices of triangles in the figure.
Step 4: State clearly any assumptions you make which will enable you to use right angled triangles or
properties of other geometric figures.
Step 5: Choose an appropriate trigonometric ratio and use it to generate an equation connecting the
quantities. On some occasions more than one equation may be needed.
Step 6: Solve the equation(s) to find the unknown.
Step 7: Answer the question in words.C PROBLEM SOLVING [8.1]
M
MoonA
Earth0.25°
r
rWhat to do:What to do:IGCSE01
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_15\322IGCSE01_15.CDR Friday, 31 October 2008 9:54:47 AM PETER