A shopkeeper stands at the first-floor stockroom window, \(2.4\) m above the yard, and looks down at a delivery van parked below. The angle of depression to...
Question 1 Report
A shopkeeper stands at the first-floor stockroom window, \(2.4\) m above the yard, and looks down at a delivery van parked below. The angle of depression to the van is \(27^{\circ}\).
Find how far the van is parked from the wall directly beneath the window, correct to 3 significant figures. (3)
Answer Details
The angle of depression from the window down to the van equals the angle of elevation from the van up to the window, because the horizontal at the window and the horizontal at ground level are parallel lines cut by the same line of sight (alternate angles). In the right-angled triangle formed by the wall, the ground, and the line of sight, the \(2.4\) m height is opposite this angle and the distance \(x\) is adjacent to it, so the tangent ratio is used.
\[ \tan 27^\circ = \frac{2.4}{x} \] [1 mark]
\[ x = \frac{2.4}{\tan 27^\circ} \] [1 mark]
\[ x = 4.71 \text{ m (3 s.f.)} \] [1 mark]
Because the height is fixed and the angle is fairly small, the van must be several times further away than the window is high, which \(4.71\) m against \(2.4\) m confirms.
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