Question

The top of a broken tree touches the ground at a distance of 8 m from its base. If the tree is broken at a height of 6 m from the ground, then the actual height of the tree is ____

Answer 1

Step-by-step explanation:

Let A'CB represents the tree before it broken at the point C, and let the top A' touches and the ground at A after it before.

then \Delta ABC\ ΔABC is a right angle triangle, right angles at B.

AB = 12 cm

BC = 5 cm

using Pythagoras theorm,

\left(AC\right)^2\ =\ \left(AB\right)^2\ +\left(BC\right)^2(AC)

2

= (AB)

2

+(BC)

2

\left(AC\right)^2\ =\ \left(12\right)^2\ +\ \left(15\right)^2(AC)

2

= (12)

2

+ (15)

2

\left(AC\right)^{2\ }=\ 144\ +25(AC)

2

= 144 +25

\left(AC\right)^2\ =\ 169(AC)

2

= 169

AC = 13 cm

thus, the total height of the tree

AC+CB

= 13+5 = 18cm