Question

IF in triangle ABC, ∠B = 135 AB = 15 & BC = 12 then find the area of ABC

Answer 1

Give : ΔABC   AB = 15  , BC = 12 ,  ∠ B = 135°

To Find :  Area of Triangle ΔABC

Solution:

Area of Triangle with two sides and included angle

= (1/2) AB * BC * Sin ∠B

AB = 15

BC  = 12

∠B  = 135°

Area of ΔABC  = (1/2) 15 (12) Sin135°

= 15 (6) Sin45°    (∵ Sin x° = Sin(180° - x°) )

= 90 Sin45°

Sin45°  = 1/√2

= 90 / √2

= 45√2

Area of ΔABC  =   45√2 sq units

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