A tree is broken at certain height and its upper part 9 -2 m long not completely separated meet the ground at an angle of 45- Find the height of the tree before it was broken and also find the distance from the root of the tree to the point where the top of the tree meets the ground-

The given situation can be represented by the figure below cos(∠CAB) = AB/AC ⇒ AB = ACA cos (∠CAB) = 9 √(2)× cos 45^∘ = 9m ∴ distance of the point from root i ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Range of Trigonometric Ratios from 0 to 90 Degrees

A tree is bro...

Question

A tree is broken at certain height and its upper part 9 $\sqrt{2}$ m long not completely separated meet the ground at an angle of $45^{\circ}$ . Find the height of the tree before it was broken and also find the distance from the root of the tree to the point where the top of the tree meets the ground.

Open in App

Solution

The given situation can be represented by the figure below

$c o s (∠ C A B) = \frac{A B}{A C} \Rightarrow A B = A C A c o s (∠ C A B) = 9 \sqrt{2} \times c o s 45^{\circ} = 9 m ∴ d i s t a n c e o f t h e p o i n t f r o m r o o t i s 9 m A l s o s i n (∠ C A B) = \frac{B C}{A C} \Rightarrow B C = s i n (∠ C A B) \times A C = s i n 45^{\circ} \times 9 \sqrt{2} = 9 m ∴ t o t a l h e i g h t b e f o r e b r e a k i n g = 9 + 9 \sqrt{2} = 9 (1 + \sqrt{2}) m$

Suggest Corrections

Similar questions

Q. The upper part of a tree, broken by wind in two parts, makes an angle of

30^{\circ}

with the ground. The top of the tree touches the ground at a distance of

20 m

from the foot of the tree. Find the height of the tree before it was broken

Q. A plan tree 90 ft high, is broken by the wind and its upper part meet the ground at an angle of

30^{\circ}

. Find the distance of the point where the top of the tree meets the ground, from its root:

A tree 10(2+ $\sqrt{3}$ ) metres high is broken by the wind at a height 10 $\sqrt{3}$ metres from its root in such a way that top struck the ground at certain angle and horizontal distance from the root of the tree to the point where the top meets the ground is 10 m. Find the angle of elevation made by the top of the tree with the ground.

Join BYJU'S Learning Program

A tree is broken at certain height and its upper part 9√2 m long not completely separated meet the ground at an angle of 45∘. Find the height of the tree before it was broken and also find the distance from the root of the tree to the point where the top of the tree meets the ground.

The given situation can be represented by the figure below cos(∠CAB)=ABAC⇒AB=ACAcos(∠CAB)=9√2×cos45∘=9m∴distance of the point from root is 9mAlsosin(∠CAB)=BCAC⇒BC=sin(∠CAB)×AC=sin45∘×9√2=9m∴total height before breaking=9+9√2=9(1+√2)m