Question

in triangle ABC, angle A=90 degree. if AB=7cm and BC-AC=1cm,find: sin C and tan B

Answer 1

In triangle ABC angle A=90
AB=7 cm
By Pythagoras Theorem
(AB)²=(BC)²-(AC)²
49=(BC)²-(AC)²
By using the identity(a²-b²)=(a+b)(a-b)
49=(BC+AC)(BC-AC)
Since BC-AC=1
∴49=BC+AC
  1=BC-AC
Adding the two
50=2BC
BC=25
AC=24
∴sin c=AB/BC
         =7/25
and tan b=AB/AC
              = 7/24

Answer 2

In triangle ABC angle A=90

AB=7 cm

By Pythagoras Theorem

(AB)²=(BC)²-(AC)²

49=(BC)²-(AC)²

By using the identity(a²-b²)=(a+b)(a-b)

49=(BC+AC)(BC-AC)

Since BC-AC=1

∴49=BC+AC

  1=BC-AC

Adding the two

50=2BC

BC=25

AC=24

∴sin c=AB/BC

         =7/25

and tan b=AB/AC

              = 7/24