Which pair of trigonometric values is equivalent v A. cos 113º, cos 67°
B. sin 71º, sin 19
C. cos 389, sin 38°
D. cos 65º, sin 25°

D. Cos 65°,Sin 25°

Step-by-step explanation:

Since they are a pair of complementary trigonometric ratio. Complementary angles add up to 90° and so does 65° and 25°.

Answer B. did not qualify since they are from the same trigonometric ratio i.e sin.

i pretty sure it is

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4