Question #41c0d

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Answer 1 · 2016-11-28T18:48:00

#tanx=3/4#

Draw the angle in the first quadrant. The hypotenuse will be #5# and the adjacent will be #4#, since

#cosx = "adjacent"/"hypotenuse"#

Then use the Pythagorean Theorem to solve for the remaining side, which comes out to 3.

#a^2 + b^2 = c^2#

#4^2 + b^2 = 5^2#

#16 + b^2 = 25#

#b^2 = 25 - 16#

#b^2 = 9#

#b = sqrt 9#

#b = 3#

So the side opposite to the angle #x# in the triangle is #3#. Then, since

#tan(x) = "opposite"/ "adjacent"#

you have

#tanx= 3/4#