A vehicle hoist arm in a workshop lifts a car wheel vertically by \(1.05\) m. The arm makes an angle of \(27^\circ\) with the horizontal floor. d1.05 marm27...
Question 1 Report
A vehicle hoist arm in a workshop lifts a car wheel vertically by \(1.05\) m. The arm makes an angle of \(27^\circ\) with the horizontal floor.
- Work out the horizontal distance, \(d\), the wheel moves. Give your answer correct to \(3\) significant figures. (3)
- Work out the length of the hoist arm. Give your answer correct to \(3\) significant figures. (1)
Answer Details
This question tests the tangent ratio, rearranged to find the adjacent side (horizontal distance) from a known opposite side and angle, followed by Pythagoras' theorem to find the hypotenuse.
(a) The vertical lift of 1.05 m is opposite the \( 27^\circ \) angle, and the horizontal distance \( d \) is adjacent to it:
\[ \tan 27^\circ = \frac{1.05}{d} \]
\[ d = \frac{1.05}{\tan 27^\circ} \approx 2.06 \text{ m} \ (3\text{ s.f.}) \] [3 marks]
(b) The hoist arm is the hypotenuse of the right-angled triangle with legs 1.05 m and \( d \):
\[ \text{arm} = \sqrt{1.05^2 + 2.0608...^2} \approx 2.31 \text{ m} \ (3\text{ s.f.}) \] [1 mark]
Part (b) uses the unrounded horizontal distance from part (a) rather than the rounded 2.06 m, keeping the final arm length accurate to 3 significant figures.
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