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Maths GCSE Question ?
ABC is a right-angled triangle.
P is a point on AB such that AP= 4PB
BC = 3PB
Angle ACB = 90 degrees
Show that sin B = k/5 where k is an integer.
Write down the value of k 4 marks
Please help truly stuck on last question.
1 Answer
- Anonymous1 decade agoFavorite Answer
AB = AP + PB
since AP=4PB:
AB=4PB+PB
AB=5PB
now find AC:
AB^2=AC^2+BC^2
AC^2=AB^2 - BC^2
sub in AB=5PB and BC=3PB
AC^2 = (5PB)^2 - (3PB)^2
AC^2= 25PB^2 - 9PB^2
AC^2=16PB^2
AC=4PB
Sin B = AC/AB
Sin B = 4PB/5PB
Sin B = 4/5 ..... [cancel PB]
so k=4