Question

a tree is broken at a height of 4m from the ground. its top touches the ground at a distance of 3m from the base of the tree what is the original length of the tree​

Answer 1

Step-by-step explanation:

Let A’CB be the tree before it broken at the point C and let the top A touches the ground at A after it broke. Then ΔABC is a right angled triangle, at B.

AB = 3m, BC = 4m

Using Pythagoras theorem,

(AC)² = (AB)²+(BC)²

(AC)² = 3² +5²

(AC)² = 9+25

(AC)² = 34

AC = √34

AC = 5.83m

hence the original length of tree = AC+BC

= 5.83+ 5

= 10.83m

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I hope that it will help you...., thanks

Answer 2

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$ㅤㅤㅤ \tan( \alpha ) = \frac{perpendicular}{base} \\ \tan(30 ) = \frac{BC}{AC} \\ \\ ㅤㅤ \frac{1}{ \sqrt{3} } = \frac{BC}{3} \\ BC = \frac{3}{ \sqrt{3} } \\ BC = \frac{3}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\BC = \frac{3 \sqrt{3} }{3 } \\ {{\underline{ \boxed{BC = \sqrt{3} }}}}$