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A Tree Breaks Due to the Storm and the Broken Part Bends So that the Top of the Tree Touches the Ground Making an Angle of 30° with the Ground. the Distance from the Foot of the Tree to the Point Where the Top Touches the Ground is 10 Metres. Find the Height of the Tree. - CBSE Class 10 - Mathematics

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Question

A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.

Solution

Let AB be the tree of height h. And the top of the tree makes an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 10M.

lET bc = 10 And ∠ACB = 30°

Here we have to find the height of the tree.

Here we have the corresponding figure

So we use trigonometric ratios.

In a triangle ABC

`=> tan C = (AB)/(BC)`

`=> tan  30^@ = (AB)/((BC)`

`=> 1/sqrt3 = h/10`

`=> h = 10/sqrt3`

Now in tiangle ABC we have

`sin 30^@ = h/(AC)`

`=> 1/2 = 10/(sqrt3 AC)`

`=> AC = 20/sqrt3`

So the length of the tree is

` = AB + AC`

= h + AC

`= 10/sqrt3 + 20/sqrt3`

`= 10sqrt3`

= 1.73

Hence the height of tree is 17.3 m

  Is there an error in this question or solution?

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Solution A Tree Breaks Due to the Storm and the Broken Part Bends So that the Top of the Tree Touches the Ground Making an Angle of 30° with the Ground. the Distance from the Foot of the Tree to the Point Where the Top Touches the Ground is 10 Metres. Find the Height of the Tree. Concept: Heights and Distances.
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