Question

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.

Answer 1

22.9 feet

Step-by-step explanation

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Answer 2

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

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.