In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=73°, and YZ = 75 feet. Find the length of ZX to the nearest tenth of a foot.

XZ is 22.9 ft in length, to the nearest tenth of a foot.

Step-by-step explanation:

Draw and label this right triangle.  We know it's a right triangle because <Z = 90.  Side ZX (the goal of this problem) is one leg of this right triangle, and YZ (75) is the other.  <Y is the difference when the sum of the other two angles is subtracted from 180:  <Y = 180 - (73 + 90), or 90 - 73, or 17.  Then:

tan Y = tan 17 = opposite side / adjacent side.  Then the unknown side XZ is:

XZ = 75*tan 17, or

XZ = 75*0.3057 = 22.93, or, to the nearest tenth of a foot, 22.9 ft

XZ is 22.9 ft in length, to the nearest tenth of a foot.

-1/2 +2

step-by-step explanation: