If \(\sin θ = \frac{8}{{17}}\), then find the value of tan θ. 

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 1)
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  1. \(\frac{{15}}{{17}}\)
  2. \(\frac{8}{{15}}\)
  3. \(\frac{{15}}{8}\)
  4. \(\frac{{17}}{{15}}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{8}{{15}}\)
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Detailed Solution

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Given:

\(\sin θ = \frac{8}{{17}}\)

Concept used:

(H)Hypotenuse2 = (P)Perpendicular2 + (B)Base2

Calculation:

F3 SSC Arbaz 8-8-2023 D16

sinθ = P/H

So, H2 = P2 + B2

⇒ 172 = 82 + B2

⇒ 289 = 64 + B2

⇒ 225 = B2

⇒ 15 = B

Now,

tanθ = P/B

So, tanθ = \(\frac{8}{{15}}\)

∴ The required answer is \(\frac{8}{{15}}\).

 Shortcut Trick

sinθ = 8/17 = P/H, we know the triplet P = 8, B = 15, H = 17

Now, tanθ = P/B So, tanθ = 8/15

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