a) In △ ABC , ∠B = 90⁰ , AB = 12 , BC = 9 and BD is a median. Find l(AC) and l(BD).
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Answer:
△ABC is right angled △,∠B=90°
BD⊥AC
AB=3,AC=5
By Pythagoras theorem,
AB
2
+BC
2
=AC
2
⇒BC
2
=AC
2
−AB
2
=5
2
−3
2
⇒BC=4
In △ABC,
∠B=90°,AB=3,BC=4,AC=5
sinC=
AC
AB
=
5
3
→1
In △BDC
∠BDC=90°,BC=4
sinC=
BC
BD
→2
Comparing 1 and 2
5
3
=
4
BD
⇒BD=3.4
solution
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