Page 42 - Trigonometry

Example 12

Referring to the diagram above, houses 2, 3 and 4 are
on the same latitude. Houses 1 and 3 are on the same

longitude. The separation of houses 2 and 4 is D km.
The angles between latitude and longitude for houses

2 and 3 are known, derive an expression for the

distance between houses 1 and 3.

Draw the triangle as shown

on the left. The known

angles are X and Y and the
distance house 1 to house 2

is A and the distance

between house 1 and house 4 is B. The angle at the
apex of the triangle is given by,

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