Question

Lorah is considering cutting down a tall tree in her front yard, but she is worried it might be tall enough to fallon the house when coming down. She knows that the base of the tree is 50 feet from her house. Equipped with onlya 12 inch ruler, she stands at the edge of her house, holding the ruler I foot from her eye. She lines the bottom ofthe ruler up with the base of the tree, and sees that the top of the tree lines up with a point 9 inches high on theraier. Wher house be far enough away from the falling tree?

Answer 1

She has to find if the tree is tall enough to fall into her house.

She is using a 12-inches ruler to find proportions. We can draw this as:

The triangle that can be drawn using as vertices the base of the tree, the top of the tree and the house is similar to the triangle formed by the rule and the the distance of 1 ft.

We can see that as the height of the ruler that indicates the top of the tree is smaller than the foot, we know that the height H of the tree is smaller than the distance D from the house to the tree, in the same proportion.

We can calculate the height of the tree using the following proportion:

`\begin{gathered} (H)/(D)=\frac{9\text{ in}}{1\text{ ft}} \\ \frac{H}{50\text{ ft}}=\frac{9\text{ in}}{12\text{ in}}=(3)/(4) \\ H=50\text{ ft}\cdot(3)/(4) \\ H=37.5\text{ ft} \end{gathered}`

Answer: The house is far enough, as the height of the tree is less than 50 ft (it is 37.5 ft)