Question

If tan θ = \(\frac {3}{4}\) then the value of sinθ is _________

(a) \(\frac {3}{5}\)

(b) \(\frac {4}{4}\)

(c) \(\frac {3}{4}\)

(d) \(\frac {-3}{5}\)

This question was posed to me during an interview.

My question is from Trigonometric Ratios topic in portion Trigonometry of Mathematics – Class 10

Answer 1

Correct option is (a) \(\frac {3}{5}\)

The best I can explain: tanθ = \(\frac {BC}{AC} = \frac {3}{4} = \frac {3k}{4k}\)

Hence, BC = 3k, AC = 4k

Using Pythagoras theorem

AB^2 = AC^2 + BC^2

AB^2 = 4k^2 + 3k^2

AB = 5k

sinθ = \(\frac {BC}{AB} = \frac {3k}{5k} = \frac {3}{5}\)