BRAINLIEST AND 50 POINTS FOR THE ACTUAL RESPONSIBLE ANSWERS

Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown:

A support structure is shown in which a right triangle PQR is formed with the right angle at Q.

Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer, stating the theorem you used. Show all your work. (5 points)

Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth. Show all your work. (5 points)

Part A: A right triangle is formed, so we can use the Pythagoren theorem to solve for the length of rod PR. The Pythagoren theorem is a^2 + b^2 = c^2, with PR being c^2, and PQ and QR being a^2 and b^2 (interchangeably). So, we plug in the lengths and get the equation 14^2 + 8^2 = c^2. This is equal to 144 + 64 = c^2. Simplified, we have 208 = c^2. Getting the square root of both sides, we find that c is equal to approximately 16.12451549... feet.

Part B: Now we are solving for a side length rather than the hypotenuse. We can use the Pythagorean theorem here too. We have: a^2 + 14^2 = 17^2. We solve and get a^2 + 144 = 289. Simplified, a^2 = 145. The square root of 145 is approximately 9.64365076... feet, our answer.

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