a tree breaks in a storm at a point 7ft above the ground. the broken part forms a 20 degree angle with the ground. how tall was the tree
Draw a diagram. If the height of the tree was h, then
7/(h-7) = sin20°
sin20 = 7/r
r = 7/sin20 = 20.5 Ft.
h = 7 + 20.5 = 27.5 Ft.
To find the height of the tree, we can use trigonometry and the angle provided. Let's consider the broken part of the tree as a right-angled triangle.
In a right triangle, the opposite side length is the height of the tree (h), and the adjacent side length is the distance from the point of break to the base of the tree (7ft).
We can use the tangent function to relate the angle (20 degrees) to the sides of the triangle:
tan(angle) = opposite / adjacent
tan(20 degrees) = h / 7ft
Next, we can solve for the height of the tree (h):
h = tan(20 degrees) * 7ft
Using a calculator:
h ≈ 2.41 * 7ft
h ≈ 16.87ft
Therefore, the tree was approximately 16.87ft tall.
To determine the height of the tree, we can use trigonometry. We'll need to apply the concept of tangent since we have the adjacent side (the height of the broken part) and the angle.
Let's set up the trigonometric equation:
tangent(angle) = opposite / adjacent
In this case, the adjacent side is the height of the broken part, and the opposite side is the height of the tree. The given angle is 20 degrees, and the adjacent side is 7 feet.
Using the tangent function, our equation becomes:
tan(20 degrees) = height of the tree / 7 feet
To find the height of the tree, we need to isolate the variable. Multiply both sides of the equation by 7 feet:
7 feet * tan(20 degrees) = height of the tree
Now, let's calculate the solution:
Using a calculator, find the tangent of 20 degrees:
tan(20 degrees) ≈ 0.36397
Multiply it by 7 feet:
0.36397 * 7 feet ≈ 2.54779 feet
Therefore, the height of the tree is approximately 2.55 feet.