1. The tic-tac-toe method for solving problems involving similar triangles
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2. They show two different ways of solving the same problem.
Look at Worked examples 13 & 14 on page 149 of your textbook Maths Quest 9.
They show two different ways of solving the same problem.
This PowerPoint shows a different way to solve this problem.
It is called the tic-tac-toe method.
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3. A 1. 5 metre pole casts a shadow 3 metres long, as shown (in textbook)
A 1.5 metre pole casts a shadow 3 metres long, as shown (in textbook). Find the height of a building that casts a 15 metres long shadow at the same time of the day.
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4. Start by drawing a tic-tac-toe (noughts & crosses) grid and place an X in the middle.X
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5. Complete the table by reading the problem
Complete the table by reading the problem. First find what you want to find out (X). ? X

6. A 1. 5 metre pole casts a shadow 3 metres long, as shown
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Height X
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7. Now find the other object in the problem
Building ?
Height X

8. A 1. 5 metre pole casts a shadow 3 metres long, as shown
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
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9. Now find the other feature of the two objects
Building
Pole
Height X ?

10. Building Pole Height X Shadow
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
Shadow
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11. Now fill in the grid with the information you are given in the problem
Building
Pole
Height X
Shadow

12. Building Pole Height X 1.5 Shadow
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
1.5
Shadow
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13. Building Pole Height X 1.5 Shadow 3
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
1.5
Shadow 3
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14. Building Pole Height X 1.5 Shadow 15 3
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
1.5
Shadow 15 3

15. Building Pole Height X 1.5 Shadow 15 3
A 1.5 metre pole casts a shadow 3 metres long, as shown. Find the height of a building that casts a 15 metres long shadow at the same time of the day.
Building
Pole
Height X
1.5
Shadow 15 3
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16. Use the shadow lengths to find the scale factor
Building : Pole
= 15 : 3
= 5 : 1
Building
Pole
Height X
1.5
Shadow 15 3
x 5
So the shadow of the building is 5 times bigger than the shadow of the pole
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17. Building Pole Height X 1.5 Shadow 15 3
Now multiply the pole height by the scale factor to find X the height of the building
Building
Pole
Height X
1.5
Shadow 15 3
x 5
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18. X = scale factor x 1.5
= 5 x 1.5
= 7.5
So the height of the building is 7.5 metres
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