Questions: What is the length of the hypotenuse? If necessary, round to the nearest tenth. c= meters

Solution Steps

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

$c^2 = a^2 + b^2$

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

We are given that one side has length $a=4.1$ m and the other side has length $b=6.6$ m. We want to find the length of the hypotenuse, c. Substituting the given values into the Pythagorean theorem, we have:

$c^2 = 4.1^2 + 6.6^2$ $c^2 = 16.81 + 43.56$ $c^2 = 60.37$

To find $c$, we take the square root of both sides of the equation: $c = \sqrt{60.37} $ $c \approx 7.7698 \text{ m}$

Rounding to the nearest tenth gives:

$c \approx 7.8 \text{ m}$

Final Answer: The length of the hypotenuse is approximately 7.8 meters.