PLZ HEEELLPPP Use the tangent ratio to find the size of the angle marked x, correct to the nearest degree.

41°

Step-by-step explanation:

SOHCAHTOA

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

tanx = opp / adj

opposite from angle x is 12 centimeter side

adjacent to angle x is 14 centimeter side

the other side is the hypotenuse because it is opposite the right angle

tanx = 12 / 14

use the inverse tangent button (usually press 2nd or shift on calculator and then press tangent button):

Type in calculator:

answer for #1 is c

answer for #2 is d

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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