Question
Download Solution PDFIf \(\sin θ = \frac{8}{{17}}\), then find the value of tan θ.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\sin θ = \frac{8}{{17}}\)
Concept used:
(H)Hypotenuse2 = (P)Perpendicular2 + (B)Base2
Calculation:
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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