Question

!! Please help!!

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. The length of PQ is shown as 14 feet, and the length of QR is shown as 8 feet..

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)

Answer 1

A). PR = 16.13 ft

B). QR = 9.64 ft

Step-by-step explanation:

Part (A).

From the figure attached,

ΔPQR is a right triangle,

m(PQ) = 14 ft

m(QR) = 8 ft

By applying Pythagoras theorem,

Hypotenuse² = (Leg 1)² + (Leg 2)²

(PR)² = (PQ)² + (QR)²

(PR)² = (14)² + (8)²

PR = √260

= 16.125

≈ 16.13 ft

Part (B).

If PR = 17 feet

and PQ = 14 feet

By applying Pythagoras theorem in ΔPQR,

PR² = PQ² + QR²

(17)² = (14)² + (QR)²

(QR)² = 289 - 196

QR = √93

= 9.644

≈ 9.64 ft