NECO 2023 · Paper 1 · Q47

Trigonometric ratios

A ladder $x$ metres long leans against a vertical pole of $12\text{ m}$ , reaching its top and making an angle of $54^\circ$ with the horizontal ground. Calculate $x$ , correct to three significant figures.

Worked solution (try it first)

The ladder is the hypotenuse, and the 12 m pole is opposite the $54^\circ$ angle at the ground.
So $\sin54^\circ = \dfrac{12}{x}$ .
Rearrange: $x = \dfrac{12}{\sin54^\circ}$
$= \dfrac{12}{0.8090}$
$\approx 14.83$ .
To three significant figures, $x = 14.8$ m, option B.

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