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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° 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:
- Height of the tree = AB + AC
- Trigonometric ratio which involves AB, BC and ∠C is tan θ, where AB can be measured.
- Trigonometric ratio which involves AB, AC and ∠C is sin θ, where AC can be measured.
- Distance between the foot of the tree to the point where the top touches the ground = BC = 8 m
In triangle ABC,
tan C = AB / BC
tan 30° = AB / 8
1/√3 = AB / 8
AB = 8 / √3
sin C = AB / AC
sin 30° = (8/√3) / AC
1/2 = 8/√3 × 1 / AC
AC = 8/√3 × 2
AC = 16 / √3
Height of tree = AB + AC
= 8/√3 + 16/√3
= 24/√3
= 24 × √3 / √3 × √3. [On rationalizing ]
= (24√3) / 3
= 8√3
So, the height of tree is 8√3 meters.
☛ Check: NCERT Solutions Class 10 Maths Chapter 9
Video Solution:
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° 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.
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 2
Summary:
If a tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it and the distance between the foot of the tree to the point where the top touches the ground is 8 m, then the height of the tree is 8√3 m.
☛ Related Questions:
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