In the given diagram, the length of CD is 12.7 cm
Trigonometry
From the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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