Calculating distance

Calculating distance

Pencil and paper
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This task is about using trigonometry to find missing lengths.
  calculating-distance-diagram-1.png     [Not drawn to scale]
 
a)  Chris is flying a kite on a 25 metre (m) string. The string is at an angle of 74°.
     How high off the ground is the kite?
     Show your working.
 
 
 
q = __________ metres
 

calculating-distance-diagram-2.png     [Not drawn to scale]
b)  Sue swam across a river that is 32 metres (m) wide. The current took her off course by 9°.
     How far down the river did the current taken her by the time she got to the other side?
     Show your working.
 
 
 
r = __________ metres

 

calculating-distance-diagram-3.png      [Not drawn to scale]
c)  Alex sailed his yacht south-west at 45° for 36 kilometres (km).
     How far south of his starting point is Alex's yacht now?
     Show your working.
 
 
 
s = __________ kilometres
Task administration: 
This task can be completed with pencil and paper.
Level:
6
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
trigonometry, right angled triangles, cosine, sine, tangents
Description of task: 
Students use trigonometry to find missing distances in three everyday problems.
Answers/responses: 

 

Y11 (03/2000)

a)

q = 25 sin 74° or sin 74° =
[Accept q = 25 cos 16°.]

24.03 (2 d.p.)
[Accept answers between 24 and 24.03.]

difficult


difficult

b)

r = 32 tan 9° or tan 9° =
[Accept r = 32 ¸ tan 81°.]

5.07 (2 d.p.)
[Accept answers between 5 and 5.1.]

very difficult


difficult

c)

s = 36 cos 45° or cos 45° =
[Accept s = 36 sin 45°.]

25.46 (2 d.p.)
[Accept answers between 25 and 25.57.]

difficult


difficult

Accept the second part of each of a) to c) if an incorrect trigonometry ratio is correctly evaluated.

Accept if an alternative correct method of solution is used (e.g., the sine rule).

Diagnostic and formative information: 
 

Common error

Likely reason

a) to c)

Various

Uses wrong trigonometric function.

a)
b)
c)

0.75 × 25 = 18.5
0.09 × 32 = 2.88
0.45 × 36 = 16.2

Does not use a trigonometric function.