In ΔABC, the measure of angle B is 90
∘
. If sinA=
25
24
and AB=1.4cm, then what is the length (in cm) of side BC?
- A4.8
- B5
- C3
- D5.6
Solution & Step-by-step Explanation
In right-angled triangle ΔABC (right-angled at B):
sinA=
Hypotenuse
Perpendicular
=
AC
BC
=
25
24
Let BC=24k and AC=25k.
Using Pythagoras' theorem:
AC
2
=AB
2
+BC
2
(25k)
2
=AB
2
+(24k)
2
625k
2
=AB
2
+576k
2
AB
2
=625k
2
−576k
2
=49k
2
AB=7k
Given that AB=1.4cm:
7k=1.4⟹k=0.2
Now find the length of side BC:
BC=24k=24×0.2=4.8cm
sinA=
Hypotenuse
Perpendicular
=
AC
BC
=
25
24
Let BC=24k and AC=25k.
Using Pythagoras' theorem:
AC
2
=AB
2
+BC
2
(25k)
2
=AB
2
+(24k)
2
625k
2
=AB
2
+576k
2
AB
2
=625k
2
−576k
2
=49k
2
AB=7k
Given that AB=1.4cm:
7k=1.4⟹k=0.2
Now find the length of side BC:
BC=24k=24×0.2=4.8cm