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10th
Maths
Some Applications of Trigonometry
Heights and Distances
The angle of elevation of a...
MATHS
The angle of elevation of a jet plane from a point A on the ground is 60
∘
. After a flight of 15 second, the angle of elevation changes to 30
∘
. If the jet plane is flying at a constant height of 1500
2
m.Find the speed of the jet plane.
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ANSWER
Let D and E be the initial and final positions of the plane respectively
Consider the △ABD
tan60
∘
=
AB
BD
⇒
3
=
AB
1500
3
⇒AB=1500
Consider the △ACE
tan30
∘
=
AC
CE
⇒
3
1
=
AC
1500
3
⇒AC=4500
BC=AC−AB=4500−1500=3000m
DE=BC=3000m
i.e., the plane travels a distance of 3000 m in 15 seconds.
∴, speed of the plane =
15
3000
=200m\s.
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