WAEC 2021 · Paper 2 · Q3

(a)
A vertical pole $6\text{ m}$ high casts a shadow $9\text{ m}$ long at the same time that a tree casts a shadow $30\text{ m}$ long. Find the height of the tree.
(b)
Solve for $y$ : $\log(5y - 4) = \log(y + 1) + \log 4$ .

Worked solution (try it first)

(a)

At the same time of day, heights and shadows are in the same ratio (similar triangles): $\frac{h}{30} = \frac{6}{9}$ , so $h = 30 \times \frac23 = 20$ m.

(b)

Combine the right side: $\log(y + 1) + \log 4 = \log 4(y + 1)$ .
So $\log(5y - 4) = \log(4y + 4)$ , which gives $5y - 4 = 4y + 4$ and $y = 8$ .
Check: $5y - 4 = 36$ and $y + 1 = 9$ are positive.

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