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Question 1060929: If given the value for tan Θ, would you be able to find the value of sec Θ without using the measure for Θ? Keep the tangent and secant of a right triangle in mind when answering this question.
I know that if solely sec Θ is given, then there is not enough details to solve the problem, but why else?
Thanks.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Given a right triangle with sides x,y,z where z is the hypotenuse and x is the altitude, theta has sides yz
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tan(theta) = (x/z) * (1/(y/z) = (x/z) * (z/y)
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sec(theta) = z/y
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(z/y) = tan(theta) / (x/z) = (tan(theta) * z) / x
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tan(theta) = c, where c is a real number
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write c as a ratio a/b where x = a and y = b and z = square root(x^2 + y^2)
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