In triangle XYZ, angle Z is a right angle. If sinX=3/4, find tanY.

ANSWER[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]EXPLANATION[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex][tex]\sin(x) = \frac{3}{4} [/tex]This means the opposite side is 3 units and the hypotenuse is 4 units.We use Pythagoras Theorem to find [tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex][tex]{ |ZX| }^{2} +9=16[/tex][tex]{ |ZX| }^{2} =16 - 9[/tex][tex]{ |ZX| }^{2} = 7[/tex][tex]{ |ZX| } = \sqrt{7} [/tex][tex] \tan(x) = \frac{opposite}{adjacent} [/tex] [tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex][tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex][tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]