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Class- X-CBSE-Mathematics Some Applications of Trigonometry
CBSE NCERT Solutions for Class 10 Mathematics Chapter 9
Back of Chapter Questions
1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied
from the top of a vertical pole to the ground. Find the height of the pole, if the
angle made by the rope with the ground level is 30o (see Fig.).
Solution:
Solution:
AB represents the height of the pole.
In ∆ABC,
AB
sin 30o =
AC
1 AB
⇒ =
2 20
⇒ AB = 10
Hence, the height of pole is 10 m
2. A tree breaks due to storm and the broken part bends so that the top of the tree
touches the ground making an angle 30o with it. The distance between the foot of
the tree to the point where the top touches the ground is 8 m. Find the height of
the tree.
Solution:
Practice more on Some Applications of Trigonometry Page - 1 www.embibe.com
, Class- X-CBSE-Mathematics Some Applications of Trigonometry
Let AC be the original tree and A′B be the broken part which makes an angle of
30o with the ground.
In ∆A′BC,
BC
tan 30o =
A′C
1 BC
⇒ =
√3 8
8
⇒ BC =
√3
A′C
Again, cos 30o =
A′B
√3 8
⇒ =
2 A′B
16
⇒ A′ B =
√3
16 8 24
Hence, height of tree = A′ B + BC = + = = 8√3 m
√3 √3 √3
3. A contractor plans to install two slides for the children to play in a park. For the
children below the age of 5 years, she prefers to have a slide whose top is at a
height of 1.5 m, and is inclined at an angle of 30o to the ground, whereas for
elder children, she wants to have a steep slide at a height of 3m, and inclined at an
angle of 60o to the ground. What should be the length of the slide in each case?
Solution:
In the two figures, AC represent slide for younger children and PR represent slide
for elder children
In ∆ABC,
AB
sin 30o =
AC
1 1.5
⇒ =
2 AC
⇒ AC = 3 m
Practice more on Some Applications of Trigonometry Page - 2 www.embibe.com
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