In ∆ABC, AC = BC = 10 cm, what is the area in square cm enclosed by ∆ABC if external angle C is 150°?
Explanation:
Given external angle C = 150°
⇒ internal angle C = 180° - 150° = 30°
∴ m ∠ACB = 30°
AC = BC = 10 cm
Two sides and the angle included by them are known.
∴ Area of the triangle = 1/2 × (AC) × (BC) × sin θ
∴ Area of ∆ABC = 1/2 × (10) × (10) × sin 30° = 25 cm2. [sin 30° = 1/2]
Hence, option (e).
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