The tic-tac-toe method for solving problems involving similar triangles Click for next slide

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. Click for next slide

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. Click for next slide

Start by drawing a tic-tac-toe (noughts & crosses) grid and place an X in the middle.   X Click for next slide

Complete the table by reading the problem Complete the table by reading the problem. First find what you want to find out (X).   ? X

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 Click for next slide

Now find the other object in the problem   Building ? Height X

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 Click for next slide

Now find the other feature of the two objects   Building Pole Height X ?

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 Click for next slide

Now fill in the grid with the information you are given in the problem   Building Pole Height X Shadow

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 Click for next slide

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 Click for next slide

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

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 Click for next slide

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 Click for next slide

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 Click for next slide

X = scale factor x 1.5 = 5 x 1.5 = 7.5 So the height of the building is 7.5 metres Click to view slide show again