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#1**+2 **

First one :

We know an opposite side and an adjacent side....the tangent seems most appropriate, here

So we have

tan x = 11/9 use the tan inverse (atan) to find x

atan (11/9) = x ≈ 50.71° = 51°

Second one....

tan Y = 6/7 tan Z = 7/6

Third one :

We know an angle, the hypotenuse and we are looking for an adjacent side to the angle....the cosine is what we need

cos (26) = x / 10 multiply both sides by 10

10 cos (26) = x ≈ 9

Fourth one :

We know an angle, the adjacent side....and we are looking for the hypotenuse....the cosine, again....

cos36 = 12 / x divide both sides by cos 36......multiply both sides by x

x = 12 / cos 36 ≈ 14.8

Last one

We know an angle, an adjacent side....and we are looking for the opposite side.....the tangent seems good

tan 40 = x / 5 multiply both sides by 5

5 tan (40) = x ≈ 4.2

CPhill May 2, 2018