To find the distance the flying squirrel has to glide, we can use the Pythagorean theorem. The situation can be visualized as a right triangle, where:
- One leg of the triangle is the vertical distance from the nest to the ground, which is \( 5.9 \) meters.
- The other leg of the triangle is the horizontal distance from the base of the tree to the fallen acorn, which is \( 4.8 \) meters.
We can find the hypotenuse (the distance the flying squirrel has to glide) using the formula:
\[ c = \sqrt{a^2 + b^2} \]
Where:
- \( a = 5.9 \) meters (vertical distance)
- \( b = 4.8 \) meters (horizontal distance)
- \( c \) is the distance glided.
Now substitute the values into the equation:
\[ c = \sqrt{(5.9)^2 + (4.8)^2} \]
Calculating each term:
\[ (5.9)^2 = 34.81 \] \[ (4.8)^2 = 23.04 \]
Now, add these values together:
\[ c = \sqrt{34.81 + 23.04} = \sqrt{57.85} \]
Now, calculate the square root:
\[ c \approx 7.6 \]
So, the flying squirrel will have to glide approximately 7.6 meters.
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