Theory question 112
Trigonometry(a) Given that sin y = 8/17, find the value of 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 5/12 of the remainder, while the rest went to Adeola. In what ratio was the money shared?
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Model answer
(a) Adjacent side = √(172 − 82) = 15, so tan y = 8/15
1 + 2 tan y = 1 + 16/15 = 31/15
tan y/(1 + 2 tan y) = (8/15) ÷ (31/15) = 8/31
(b) Remainder = ₦240,000; Ada = 5/12 × 240,000 = ₦100,000; Adeola = ₦140,000
Ratio 60,000 : 100,000 : 140,000 = 3 : 5 : 7
Explanation
Draw a right-angled triangle with opposite 8 and hypotenuse 17.