Question

. In 4ABC, B = 90◦
, C = 60◦
, A = 30◦ BD ⊥ AC, BE is angle
bisector of ∠ABD where D and E are on AC. If AE = 13, find BC.

Answer 1

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