Apply Trigonometry Knowledge to 3D Shapes

 

                             

Questions

How can you find the height of this mountain?

How can this mountaineer draw an accurate map?

How did sailors navigate before GPS?

How can computers rotate images so that they can be viewed from many different directions?

 

Answer

They look at angles and sides of triangles and make connections between them.

This is pretty cool stuff really.

 

This is called Trigonometry.   A lot of the times trigonometry is applied in 3D.

Trigonometry is used to help solve problems within right angled triangles.

Trigonometry ratios - recap

   

Example

 

                          

1. Draw in the right angled triangle as shown in the example.  Then if it is helpful draw it out in 2 dimensions.

2. Label the triangles

3. Apply the correct trig ratio

4.  We have the opposite 10 cm and the adjacent 20 cm, therefore the tan ratio.

5.  10 ÷ 20 = 0.5 then tan-1 0.5 = 26.6° correct to one decimal place.

 

So time to quit the computer game (although trigonometry is used to help create them) and have a go at applying your knowledge.

 

Note:  Don't round up your answers until you have worked through the whole problem otherwise your answer may differ quite a bit.