(a) Given that sin y = \(\frac{8}{17}\) find the value of \(\frac{tan y}{1 + 2 tan y}\)
(b) An amount of N300,000.00 was shared among Otobo, Ada and Adeola. Otobo received N60,000.00, Ada received \(\frac{5}{10}\) of the remainder, while the rest went to Adeola. In what ratio was the money shared?
Explanation
x\(^2\) = 172\(^2\) - 8\(^2\)
x\(^2\) = 289 - 64
x\(^2\) = 225
x = \(\sqrt{225}\)
x = 15
tan y \(\frac{8}{15}\)
1 + 2 tan y = 1 + 2(\(\frac{8}{15}\))
= \(\frac{1}{1} + \frac{6}{15}\)
= \(\frac{15 + 16}{15} = \frac{31}{15}\)
\(\frac{\tan y}{1 + 2 \tan y}\)
= \(\frac{8}{15} \div \frac{31}{15}\)
= \(\frac{8}{15} \times \frac{15}{31} = \frac{8}{31}\)
(b) Otobo shares = N60,000
Remainder = N300,000 - N60,000
= N240,000
Ada's share = \(\frac{5}{12}\) x N240,0000
= N100,000
Adeola's share =;
= 300,000 - N160,000 = N140,000
Ratio of the money is
Otobo : Ada : Adeola
60,000 : 100,000 : 140,000
60 : 100 : 140
6 : 10 : 14
3 : 5 : 7