A stepladder in the community library leans against the shelves at 68° to the floor. The ladder is 2.6 m long and reaches a height of \(h\) metres. 2.6 mh m...
Question 1 Report
A stepladder in the community library leans against the shelves at 68° to the floor. The ladder is 2.6 m long and reaches a height of \(h\) metres.
- Find the value of \(h\), correct to 3 significant figures. (2)
Answer Details
The figure shows the ladder as the hypotenuse of a right-angled triangle, with the floor horizontal, the shelves vertical, and the 68° angle between the ladder and the floor.
- The height \(h\) is opposite the 68° angle and the 2.6 m ladder is the hypotenuse, so \(\sin 68^\circ = \frac{h}{2.6}\), giving \(h = 2.6 \sin 68^\circ = 2.6 \times 0.92718\ldots = 2.41067\ldots\). [1]
- \(h = 2.41\) m to 3 significant figures. [1]
The answer must be less than the length of the ladder, since the hypotenuse is always the longest side, and 2.41 m is duly less than 2.6 m. An answer larger than 2.6 m would signal that the ratio had been used upside down.
Multiplying by the sine, rather than dividing, is what is needed when the unknown is on top of the fraction. The steep 68° angle is why the ladder reaches nearly its full length in height.
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