Q5 of 31 Page 117

One side of a triangle is 6 centimetres and the angles at its ends are 40° and 65°. Calculate its area.

Let ABC be a triangle, with BC = 6 cm and angles at its ends are ∠ABC = 40° and ∠ACB = 65° respectively.


Draw AP ⊥ BC, such that APB and APC are right-angled triangles,


Let AP = 'h' cm


BP = 'x' cm and PC = (6 - x) cm



In ΔAPB,






…[1]


In ΔAPC






⇒ 2.1445(6 - x) = h


= h [From 1]


⇒ 12.867 - 2.556h = h


⇒ 3.556h = 12.867


⇒ h = 3.618 cm


Also, area of a triangle




⇒ area(ΔABC) = 3 × 3.618


= 10.854 cm2 [appx]


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