In △ABC, ∠B = 135°, AB = 5 cm and BC = 7cm. The length of AC is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 13 cm.
AC2 = AB2 + BC2 - 2 × AB × BC × cos(B)
⇒ AC2 = (5√2)2 + 72 - 2 × 5√2 × 7 × cos(135°)
= 50 + 49 - 70√2 × cos(135°)
= 99 - 70√2 × (-1/√2)
= 99 + 70
= 169
⇒ AC = √169 = 13 cm