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Question
A researcher wants to determine the width of a pond from east to west, which cannot be done by actual measurement. From a point P, he finds the distance to the eastern-most point of the pond to be 8 km, while the distance to the westernmost point from P to be 6 km. If the angle between the two lines of sight is 60°, find the width of the pond
Solution
A – be the easternmost point on the pond and
B – be the westernmost point on the pond.
AB – Width of the pond
P – Point of observation.
The distance of A from P = 8 km
Distance of B from P = 6 km
Angle between the directions PA and PB
∠APB = 60°
In ∆PAB,
Using cosine formula
AB2 = PA2 + PB2 – 2PA . PB . cos∠APB
AB2 = 82 + 62 – 2 × 8 × 6 . cos 60°
= `64 xx 36 - 96 xx 1/2`
= 100 – 48
= 52
AB = `sqrt(52)`
= `sqrt(4 xx 13)`
AB = `2sqrt(13)` k.m.
Width of the pond = `2sqrt(13)` k.m.
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