Question
Download Solution PDFIf A + B = 90° and sin A = \(\frac{3}{5}\), then the value of tan B is __________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA + B = 90°
SinA = 3/5
Formula Used:-
Hypotenuse2 = Perpendicular2 + Base2
Sinθ = Perpendicular(P)/Hypotenuse(H)
tanθ = Perpendicular/Base(B)
tan(90° - A) = cotA
Calculation:-
SinA = 3/5 = P/H
⇒ P = 3k and H = 5k [Where k is a constant]
Base = √(H2 - P2)
⇒ Base = √(5k)2 - (3k)2
⇒ Base = 4k
⇒ tanA = P/B
⇒ tanA = 3k/4k = 3/4
⇒ tan(90° - B) = 3/4
⇒ cotB = 3/4
⇒ tanB = 4/3
∴ The required answer is tanB = 4/3.
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