Question

A bird was sitting 8 meters from the base of a tree and flew 9.3 meters to reach the top of the tree. How tall is the tree? If necessary, round to the nearest tenth.

PLEASEEEEE HELPPPPPP

Answer 1

The height of the tree is approximately 4.7 meters. Rounding to the nearest tenth, the tree is approximately 4.7 meters tall.

To determine the height of the tree, we can use the Pythagorean theorem since we have a right-angled triangle formed by the bird, the base of the tree, and the top of the tree. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this scenario, the horizontal distance from the bird to the base of the tree represents one side of the triangle (8 meters), the vertical distance from the base to the top of the tree represents the other side (the height of the tree, let's call it h), and the diagonal path the bird took represents the hypotenuse (9.3 meters).

Using the Pythagorean theorem:

`\[ 8^2 + h^2 = 9.3^2 \]`

`\[ 64 + h^2 = 86.49 \]`

`\[ h^2 = 86.49 - 64 \]`

`\[ h^2 = 22.49 \]`

`\[ h = √(22.49) \]`

`\[ h \approx 4.7 \]`