Tracking sports professionals

Tracking sports professionals

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This task is about using the Pythagoras theorem to work out lengths of diagonals.
 
Olympic diagonals diagram
The Black Ferns are training using a rectangle that is 60 m long by 20 m wide.
 
a)
Ruby Tui crosses from point X to point Y.
Use Pythagoras' theorem to work out the length of the diagonal XY.
Show your working.
 
 
 
 

 

 
 
 
 
XY = __________ m
 
b)
She then crosses from point F to point E, and then to point M.
Point E is half way along the other side, and points F and M are 6 m in from each side.
Work out how far she travels between these points.
Show your working.
 
 
 
 
 
 
 
 
 
FE + EM = __________ m
Task administration: 
This task can be completed with pencil and paper.
Level:
6
Curriculum info: 
Maths, Geometry and Measurement, Shape
Keywords: 
trigonometry, pythagoras theorem, right angled triangles
Description of task: 
Students find out the length of the sides of triangles using Pythagoras' theorem, and show their working.
Answers/responses: 

 

Y11 (03/2000)

a)

Shows at least 1 of:

•   XY2 = 602 + 202
•   XY =

63.25 (2 d.p.) [Accept answers between 63 and 63.3]

moderate


 

moderate

b)

Uses side lengths of 20 and 24 (or 20 and 48) in 
the calculations.

Shows at least 1 of:

•   FE2 = 202 + 242
•   FE =
•   EM2 = 202 + 242
•   EM =
•   Accept if trigonometry used correctly,
     e.g., tan θ = 24/20
     Therefore q = 50.2 o
     FE = 20 ÷ cos 50.2 o
[Accept if wrong side lengths are used but Pythagoras is correctly applied.]

62.48 (2 d.p.)
[Also accept:
•   Answers between 62 and 62.5.
•   Answer to FE + answer to EM if Pythagoras'
     theorem was used in the calculations.]

difficult


very difficult

 

 

 

 

 

 


very difficult