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Question

An observer at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 45 and 60 respectively. Find the width of the river. Write the answer correct to the nearest whole number. [3 MARKS]

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Solution

In ΔOMA

tan 45=OMAM

I=250x {tan 45=1}



x=250 m

In ΔOMB, tan 60=250y

3=250yy=2503=2501.73

y=144.34

Width of river = x + y = 250 + 144.34

= 394.34 m

In Δ ABC [12 MARK]

tan 60=240x

3x=240

x=2403(1) [1 MARK]

In Δ ABD

tan 45=240y

1=240y

y=240 [1 MARK]

Width of river =240803

=80(33)

=101.44

=101 m [12 MARK]


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