In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=65°, and ZX = 4.8 feet. Find the length of YZ to the nearest tenth of a foot.
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Hi there! :)
Find the central angle using a ratio in regards to angle and circumference.
The radius is 27 units, so use the following equation to calculate circumference:
C = 2rπ
Therefore:
C = 2(27)π = 54π
Since we have the total circumference, we can write the following proportion:
Cross multiply:
54πx = 6480π
Divide both sides by 54π to isolate for x:
x = 120°