Question

question 3
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.
feet
question 4
an athlete runs the trails in a park.
trail a forms a rectangle around the perimeter of the park.
the short sides are 0.5 miles and the long sides are 1.5 miles long.
trail b and trail c form diagonals from one corner of the park to another corner.

Explanation:

For Question 3:

Step1: Identify right triangle sides

Pole height $a=8$ ft, base distance $b=5$ ft.

Step2: Apply Pythagorean theorem

Wire length $c = \sqrt{a^2 + b^2}$

Step3: Calculate and round

$\sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.4$

Step1: Use rectangle perimeter formula

Perimeter $P = 2(l + w)$

Step2: Substitute side lengths

$l=1.5$ miles, $w=0.5$ miles

Step3: Compute total perimeter

$P = 2(1.5 + 0.5) = 2(2) = 4$

Answer:

9.4 feet

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For Question 4: