A dead tree was struck by lightning, causing it to fall over at a point 10 ft up from the base of the tree.
If the fall treetop forms a 40 angle with the ground, about how tall was the tree originally?
fallen*
To determine the original height of the tree, we can use trigonometry. The fallen tree forms a right triangle with the ground. The vertical height of the fallen tree is the distance from the point where it fell to the base of the tree, and the hypotenuse of the triangle is the original height of the tree.
Now, we know that the fallen tree forms a 40° angle with the ground. So, the adjacent side of the triangle (the distance from the point where it fell to the base of the tree) is 10 ft, and we need to find the length of the hypotenuse (the original height of the tree).
We can use the trigonometric function cosine to solve for the hypotenuse:
cos(40) = adjacent / hypotenuse
Rearranging the equation, we have:
hypotenuse = adjacent / cos(40)
Calculating the value, we get:
hypotenuse = 10 / cos(40)
Using a calculator, the value of cos(40) is approximately 0.766. Therefore:
hypotenuse = 10 / 0.766 ≈ 13.05 ft
Hence, the original height of the tree was approximately 13.05 feet.