Given that sin x = 0.8, find tan x. Solve by using right-angled triangled.

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bridgetrbcs eNotes educator| Certified Educator

If sin is .8 which is 4/5, that tells us that the opposite side is a length of 4 and the hypotenuse is a length of 5 (or at least a multiple of those). 

If we are using a right triangle where a^2 +b^2 = c^2, we could find the missing side by filling in 4 for a and 5 for c. 

  • 4^2 + b^2 = 5^2
  • 16 +b^2 = 25
  • b^2 = 9 (Subtract 16 from both sides.)
  • b = 3 (Take the square root of both sides.)

If b = 3 and b is the adjacent side, we have completed our triangle.  Remember that tan X = opp/adj so tan X = 4/3.  I would leave this as a fraction since it becomes a repeating decimal if you try to change it.  Hope this helps!