Answer:
The original height of tree is 18 m.
Step-by-step explanation:
Consider the correct question is "A tree is broken at the height of 5m from the ground and its top touches the ground at a distance of 12m from the Base of the tree. Find the original height of the tree."
A tree is broken at the height of 5m from the ground.
Let the height of the tree is (x+5) m.
After broken, it will form a right angle triangle with hypotenuse x, base 12m and perpendicular 5 m.
Using Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]x^2=12^2+5^2[/tex]
[tex]x^2=144+25[/tex]
[tex]x^2=169[/tex]
Taking square root on both sides.
[tex]x=13[/tex]
Height of tree = [tex]x+5=13+5=18\text{ m}[/tex]
Hence, the height of tree is 18 m.
Answer:
18 cm.
Step-by-step explanation:
Please find the attachment.
Let ABC be the height of tree and tree is broken at point B such that top A touches the ground.
Now, we will use Pythagoras theorem to solve for length AB as AB is hypotenuse of right triangle.
[tex]AB^2=BC^2+AC^2[/tex]
[tex]AB^2=5^2+12^2[/tex]
[tex]AB^2=25+144[/tex]
[tex]AB^2=169[/tex]
Now, we will take positive square root of both sides as:
[tex]\sqrt{AB^2}=\sqrt{169}[/tex]
[tex]AB=13[/tex]
The total length of the tree would be [tex]AB+BC\Rightarrow 13+5 =18[/tex].
Therefore, the original height of the tree was 18 cm.
