Heights And Distances Trigonometry Worksheet With Answers - The Institute Of Mathematical Science Page 5
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Solved Problems
1. Two ships are sailing in the sea on the two sides of a lighthouse. The
angle of elevation of the top of the lighthouse is observed from the
o
o
ships are 30
and 45
respectively. If the lighthouse is 100m high.
What is the distance between the two ships?
Solution : Let AB be the lighthouse and C and D be the positions
of the ships.
Here, we need to find CD
o
o
AB = 100m, ACB = 30
and ADB = 45
AB
1
o
= tan 30
=
=
AC = AB
3 = 100 3m
AC
3
AB
o
= tan 45
= 1 =
AB = AD = 100m
AD
Now,
CD = (AC + AD)
= (100 3 + 100)m
= 100( 3 + 1)m
= (100
2.73)m
= 273m
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