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Question
If sin A = `3/4`, calculate cos A and tan A.
Solution
Let ΔABC be a right-angled triangle, right-angled at point B.
Given that,
sin A = `3/4`
`("BC")/("AC") = 3/4`
Let BC be 3k.
Therefore, AC will be 4k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(4k)2 = AB2 + (3k)2
16k2 − 9k2 = AB2
7k2 = AB2
AB = `sqrt7k`
cos A = `("Side adjacent to ∠A")/"Hypotenuse"`
∴ cos A = `("AB")/("AC")`
= `sqrt(7k)/(4k)`
= `sqrt7/4`
tan A = `("Side adjacent to ∠A")/("Side adjacent to ∠A")`
= `("BC")/("AB")`
= `(3k)/(sqrt7k)`
= `3/sqrt7`
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