A technician bolts a diagonal support rod to a rectangular lab bench frame. The rod forms the hypotenuse of a right-angled triangle whose other two sides me...
Question 1 Report
A technician bolts a diagonal support rod to a rectangular lab bench frame. The rod forms the hypotenuse of a right-angled triangle whose other two sides measure \(8.3\) cm and \(5.7\) cm, as shown.
Work out the length of the support rod. Give your answer correct to \(3\) significant figures. (3)
Answer Details
This question applies Pythagoras' theorem to find the hypotenuse of a right-angled triangle from its two shorter sides.
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Substituting the two given lengths:
\[\sqrt{8.3^2 + 5.7^2}\][1 mark]
\[= \sqrt{68.89 + 32.49} = \sqrt{101.38}\][1 mark]
\[= 10.1 \text{ cm (3 s.f.)}\][1 mark]
The support rod is \(10.1\) cm long. Rounding only happens at the final step, after taking the square root, to avoid losing accuracy along the way.
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