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JAMB Mathematics 2018 Paper

Question : 31

Total: 62

Solution:

Concept:

The angle of depression equals the angle of elevation from the boat to the man, so use the tangent ratio in a right-angled triangle.

Explanation:

Let

x

be the distance of the boat from the base of the tree.

The height of the tree is

150\text{ cm}

Using

\tan \theta = \frac{\text{opposite}}{\text{adjacent}}

, we have:

\tan 74^\circ = \frac{150}{x}

Rearrange to solve for

x

x = \frac{150}{\tan 74^\circ}

x = \frac{150}{3.4874}

x \approx 43.01\text{ cm}

Therefore, the boat is about

43\text{ cm}

from the base of the tree.

Answer:

43\text{ cm}

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