Question
Download Solution PDFIn Δ ABC, ∠B = 135°, AB = 10√2 cm and BC = 14 cm. What is the length of AC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In Δ ABC, ∠B = 135°, AB = 10√2 cm and BC = 14 cm.
Formula used:
Using the Cosine Rule:
\(c^2 = a^2 + b^2 - 2ab \cos(C)\)
Calculations:
Let AB = c = 10√2 cm, BC = a = 14 cm, and AC = b.
∠B = 135°
Using the Cosine Rule:
\(b^2 = a^2 + c^2 - 2ac \cos(B)\)
⇒ \(b^2 = 14^2 + (10√2)^2 - 2 \times 14 \times 10√2 \times \cos(135°)\)
⇒ \(b^2 = 196 + 200 - 2 \times 14 \times 10√2 \times -\frac{1}{√2}\)
⇒ \(b^2 = 196 + 200 + 2 \times 14 \times 10\)
⇒ \(b^2 = 676\)
⇒ \(b = 26\) cm
∴ The correct answer is option (3).
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