WAEC 2019 · Paper 2 · Q12

(a)
Given that $\sin y = \frac{8}{17}$ , find the value of $\dfrac{\tan y}{1 + 2\tan y}$ .
(b)
An amount of ₦300,000.00 was shared among Otobo, Ada and Adeola. Otobo received ₦60,000.00, Ada received $\frac{5}{12}$ of the remainder, while the rest went to Adeola. In what ratio was the money shared?
Show the answer
$3 : 5 : 7$

Worked solution (try it first)

(a)

$\sin y = \frac{8}{17}$ : the adjacent side is $\sqrt{17^2 - 8^2} = \sqrt{225} = 15$ , so $\tan y = \frac{8}{15}$ .
Then $\frac{\tan y}{1 + 2\tan y} = \frac{\frac{8}{15}}{1 + \frac{16}{15}}$
$= \frac{\frac{8}{15}}{\frac{31}{15}}$
$= \frac{8}{31}$ .

(b)

After Otobo's ₦60,000, the remainder is ₦240,000.
Ada received $\frac{5}{12} \times 240\,000 =$ ₦100,000, and Adeola the rest, ₦140,000.
The ratio is $60\,000 : 100\,000 : 140\,000 = 3 : 5 : 7$ .

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