Question

In ΔABC, m∠ACB = 90°, and m∠ACD = 45°. Find CD, if BC = 3in.

Answer 1

Answer:

Step-by-step explanation:

We need to find CD

since ANGLE ACD=45

ANGLE BCD=45

COS 45=CD/CB

1/2=CD/3

so CD =3/2

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Answer 2

Answer:

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