The scale factor of the dilation that transforms the triangle is 1/3
9x1/3 is 3. 6x1/3 is 2, etc.
The base of the ladder has a length of 8 ft.
We have to draw a triangle, as the figure attached.
The hypothenuse of the triangle is the length of the ladder (17 ft).
The height on the wall that the ladder reach is the adjacent (15 ft).
The base of the ladder is our unknown quantity X.
We will use the Pythagorean theorem to express the relation between these numbers:
<u>The height of the tree is √65 or 8.06 feet</u>
Let's use the Pythagorean theorem to find out the height of the tree, this way:
Hypotenuse = length of the ladder = 9 feet
Leg 1 = Distance from the base of the tree to bottom of the ladder = 4 feet
Leg 2 = Height of the tree
Now, replacing with the real values we have:
Leg 2 ² = Hypotenuse² - Leg 1²
Leg 2² = 9² - 4²
Leg 2² = 81 - 16
Leg 2² = 65
√Leg 2² = √65
Leg 2 = √65 or 8.06 feet