Ex 9.1 Q2 - 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:-Let,
*AC be the original tree.
*BD be the broken part of tree.
'C' be the foot of tree.
'B' be the point from where tree
is broken.
Given,
Distance between the foot of tree 'C'
and point 'D' = CD = 8 m.
The broken part 'BD' makes an angle
of 30° with ground,
∴ ∠D = 30°
➙ In ∆BCD, ∠BCD = 90°
∴ tanD =
Opposite side of ∠D
/
Adjacent side of ∠D
∴ tan30° =
BC
/
CD
∴
1
/
√3
=
BC
/
8
{ ∵ tan30° = 1/√3 } ∴ BC =
8
/
√3
------- (1)➙ In ∆BCD, ∠BCD = 90°
∴ cosD =
Adjacent side of ∠D
/
Hypotenuse
∴ cos30° =
CD
/
BD
∴
√3
/
2
=
8
/
BD
{ ∵ cos30° = √3/2 } ∴ BD =
8 × 2
/
√3
∴ BD =
16
/
√3
------- (2)➙ Now,
*Original Height of tree
= AC
= Height of broken part + Height of remaining part
= AB + BC
= BD + BC {∵ AB = BD}
=
16
/
√3
+
8
/
√3
{From (1) & (2)} =
24
/
√3
*Multiplying Numerator and Denominator by √3,
=
24
/
√3
×
√3
/
√3
=
24√3
/
3
= 8√3
∴ AC = 8√3
Hence,
The height of the tree is 8√3 m.
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Try This..
✒ A ladder is leaning against a wall at an angle of 60° and reaches a height of 10 m on the wall. Find the length of the ladder.
✒ A kite is flying at a height of 60 m. The string attached to it is making an angle of 45° with the ground. Find the length of the string.
✒ A man is standing 10 m away from a pole. The angle of elevation of the top of the pole is 60°. Find the height of the pole.
❌ Common Mistakes
Using the wrong trigonometric ratio:▸ Students often confuse sin, cos, and tan.▸ Always identify the side (opposite, adjacent, hypotenuse) correctly.Rounding off too early:▸ It’s better to use full values (like √3) during calculations and only round off at the end for accuracy.Not drawing a diagram:▸ Visualizing the problem makes it 10x easier to understand and solve.▸ Always sketch the situation first.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 9.1
Ex 9.1 Q2 Class 10
Class 10 Ex 9.1 Q2
Class 10 Chap 9 Ex 9.1 Q2
Class 10 Some Applications Of Trigonometry
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