In δabc, m∠acb = 90°, and m∠acd = 45°. find cd, if bc = 3in.

3/√2 inches

Step-by-step explanation:

From the ∆ACB,

∠ACD + ∠DCB = 90°

45° + ∠DCB = 90°

∠DCB = 90° - 45°

∠DCB = 45°

Using sine rule on ∆CDB to get BC,

BC/∠CDB = CD/∠CBD

BC/sin90° = CD/sin45°

3/sin90° = CD/sin45°

3 = CD/(1/√2)

3 = √2 × CD

CD = 3/√2 inches

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