Verified answer

A ladder is placed to reach a tree house.

The height of the tree house from the ground is half the length of the ladder.

Opposite side is 1 and the hypotenuse is 2

The Sine value is 1/2. Hence the angles are 30, 60 and 90 degrees.

Hence the length from the bottom of the tree to the bottom of the ladder is

(2^2 - 1^2)^1/2 th length of the ladder which is taken as 2.

That is 1/2(3)^1/2 th part of the ladder.

H = Height of tree

L = ladder

G= length from the bottom of the tree to the bottom of the ladder

height of the tree house from the ground is half the length of the ladder

L = 2H

using Pythagorean theorem, you can find G.

a^2 + b^2 = c^2

G = a; H = b

G^2 + H^2 = 2H^2

solve for G

2H^2 + H^2 = -G^2

3H^2 = -G^2

1/ 3H^2 = G^2

to simplify any more, you would need to place actual numbers for G, H, and L.

From the right angled triangle formed

Perpendicular = h

hypotenuse = 2h

Using pythagoras

4h^2 - h^2 = base^2

3h^2 = base^2

Take positive square root

Bottom of tree to bottom of ladder is sqrt 3 [times length of ladder]