if triangle abc is an equilateral triangle of side A and D is a point on BC such that BD=1/3BC,then prove that AD=underroot7×a/3.
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Answer:
In △ABC AB=AC
⇒∠B=∠C (Angles opposite to equal sides are equal)
Now using angle sum property
∠A+∠B+∠C=180
∘
⇒80
∘
+∠C+∠C=180
∘
⇒2∠C=180
∘
−80
∘
⇒∠C=
2
100
∘
=50
∘
now ∠C+∠x=180
∘
(Angles made on straight line (AC) are supplementary)
⇒50
∘
+∠x=180
∘
⇒∠x=180
∘
−50
∘
=130
∘
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