Question

question 2
1 pts
a carpenter is cutting pieces of wood for a project.
he has a square piece of wood with side lengths of 8 inches.
he cuts the square diagonally creating two right triangles.
find the length, in inches, of the longest side of the resulting right triangle.
round your answer to the nearest tenth, if needed.

inches
question 3
1 pts
a wire is stretched from the top of an 8 - foot pole to a bracket 5 feet from the base of
the pole.
find the length of the wire. round your answer to the nearest tenth, if needed.

Explanation:

Question 2

Step1: Identify right triangle sides

The square's sides (legs of the right triangle) are both 8 inches.

Step2: Apply Pythagorean theorem

The longest side (hypotenuse $c$) is calculated as:
$$c = \sqrt{a^2 + b^2}$$
Substitute $a=8$, $b=8$:
$$c = \sqrt{8^2 + 8^2} = \sqrt{64 + 64} = \sqrt{128}$$

Step3: Calculate and round value

$$\sqrt{128} \approx 11.3$$

Step1: Identify right triangle sides

Pole height (leg) = 8 ft, distance from base (leg) = 5 ft.

Step2: Apply Pythagorean theorem

Wire length (hypotenuse $c$) is calculated as:
$$c = \sqrt{a^2 + b^2}$$
Substitute $a=8$, $b=5$:
$$c = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89}$$

Step3: Calculate and round value

$$\sqrt{89} \approx 9.4$$

Answer:

11.3 inches

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Question 3