Sine, cosine, radians
#sinerule #cosinerule #bearing #radian #arclength
Calculate the value of and :
Town is 6 km, on a bearing of 020, from town . Town is
located on a bearing of 055 from town and on a bearing of
120 from town .
Work out the distance of town from
Work out the value of
Work out the value of and
there are two possible results, because you can draw two
different triangles which satisfy the task
• These results and are connected:
In this example:
(to 3 s.f.)
Work out the possible values of and the corresponding
values of .
Work out the value of the third side:
From a point a boat sails due north for 7 km to . The boat leaves and
moves on a bearing of 100 for 10 km until it reaches .
Calculate the distance of from .
Work out the size of the angle marked with * (to 3 s.f.):
A helicopter flies on a bearing of 080 from to , where km. It
then flies for 60 km to a point .
Given that is 80 km from calculate the bearing of from .
1 side, 2 angles
2 sides, angle
2 sides, angle
Work out the area of the given triangle:
Work out the value of :
equal to .
when is in radians.
The sector of the circle radius cm
contains an angle of radians. Find the
length of the arc, giving your answers in
the form , where and are integers.
Referring to the diagram, find:
a) The perimeter of the shaded region
a) The value of when the perimeter of
the shaded region is 14 cm.
In the diagram is the diameter of a circle, centre and radius 2 cm. The
point lies on the circumference such that radians.
a) State the value, in radians, of .
The shaded region is a template for a
(b) Find the exact value of the
perimeter of the brooch.
where is in radians
Work out the area of the shaded region:
The arc of a circle, centre and radius cm, is such that
Given that the perimeter of the minor sector is 30 cm:
(a) Calculate the value of .
(b) Show that the area of the minor sector is 36 .
(c) Calculate the area of the segment enclosed by the chord
and the minor arc .
The diagram shows a triangular plot of land. The sides , and have
lengths 12, 14 and 10 m respectively.
The lawn is a sector of a circle, centre
and radius 6 m.
(a) Show that to 3 s.f.
(b) Calculate the area of the flowerbed.
In the diagram, is the diameter of a circle, centre and
radius cm, and radians.
Given that the area of is equal to
that of the shaded segment,