Question

If the pine tree´s shadow is 12 m long, with this heigth , then how far would it be from the top of the tree to the far end of the shadow? The top of the tree is blank meters from the far end of the shadow?

Answer 1

19.20 meters

Explanation

as the tree is vertical , it makes a 90 ° angle with the ground, so the tree, the shadow and the distance from the top of the tree to the end of the shadow make a rigth triangle

to find the missing value we can use the Pythagorean theorem, it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

so

$(\text{side}1)^2+(side2)^2=(hypotenuse)^2$

so

Step 1

Let

$\begin{gathered} \text{side}1=\text{ 15m} \\ \text{side 2= 12 m} \end{gathered}$

b) now, replace and solve for hypotenuse

$\begin{gathered} (\text{side}1)^2+(side2)^2=(hypotenuse)^2 \\ 15^2+12^2=h^2 \\ 225+144=h^2 \\ 369=h^2 \\ \text{square root in both sides} \\ \sqrt{369}=\sqrt{h^2} \\ 19.20=\text{ h } \end{gathered}$

therefore, the answer is

19.20 meters

I hope this helps you