National 5 - Mathematics
Supported Study 2
1. Two runners leave from the same starting point
at A and head off in different directions.
Using the information in the diagram opposite,
calculate how far apart the runners are.
A
2. A golfer is standing 120 metres from a
hole. He hits the ball, which travels a
distance of 132 metres, and ends up
9.5 metres from the hole.
Calculate, x0, the angle by which the
golfer was off target.
3. Three trees are positioned as shown opposite.
Calculate the distance between trees A and C.
4. The diagram shows the end view of the roof
of a house.
Given the information in the diagram, calculate
the height of the roof.
5. A flagpole is positioned next
to a tower 12.8 metres high.
From the top of the tower the
angle to the top of the flagpole
is 600 and from the base of the
tower the angle to the top of the
flagpole is 420.
Calculate the height of the flagpole.
6. The base of a rocking horse is in the shape of an
arc of a circle.
The circle has radius 1.85 metres and the angle made
by the ends of the base and the centre of the circle is
1400.
Calculate the length of the base of the rocking horse.
7. The beam from a torch travels a distance of
25 metres and spreads to an angle of 420.
Calculate the area covered by the beam of the
torch.
8. The boat at a carnival travels along an arc of a circle
with centre C and radius 9 metres.
The length of the arc AB is 11 metres.
Find the angle through which the boat swings.
9. The diagram shows an ornamental fish pond.
The pond is in the shape of part of a circle centre
O with a straight edge. 1000
A small fence is to be put round the outside of O
the pond.
Calculate the length of the fence.
10. A crane has a wrecking ball attached to it.
When the ball swings it makes an arc of a
circle of radius 9.8 metres.
x0
If the arc made by the ball is 13.68 metres
long, calculate the angle through which
the ball swings.
11. The diagram shows a marble chopping
board in the shape of a circle with a
straight edge.
The radii shown are each 22 centimetres.
The angle between these radii is 1100.
Calculate the distance round the outside 11
of the chopping board. 110