Question

in a triangle ABC ,if median and altitude drawn from the vertex A,then tan(b-c)is equal to​

Answer 1

Step-by-step explanation:

Let ABC be a triangle AH the height from A to BC and AM the median (M the midpoint between B and C) without loss of generality let's say that H is between B and M so we have ΔBAH and ΔMAH congruent as angles BHA and MHA are equal angle BAH and MAH are equal (per hypothesis of problem) and they share side AH. Therefore BM=HM(orHM=

2

1

BM)

So, Lets' see ΔAHC. AM is bisector therefore we have ratios

MC

MH

=

AC

AH

but MH=

2

1

MB=

2

1

MC

therefore

MC

MH

=

2

1

So AHC is a right angled triangle at H and AC=2AH. So, sinC=

2

1

and C=30

0

∠HAC=60

0

and ∠HAB=∠HAM=

2

1

∠HAC=30

0

So ∠BAC=90

0

So, ∠BAD=60

0

∠BAC=3×30

0

=90

0

.

solution