Solving 3D Problems using Pythagoras and Trigonometry

The video tutorial explains how to solve 3D problems by breaking them into 2D components, focusing on Pythagoras and trigonometry. It demonstrates solving for length CD in a cuboid and calculating the height and angle in a square-based pyramid. The tutorial emphasizes the importance of understanding Pythagoras's theorem, trigonometry, and the sine and cosine rules. It concludes with strategies for effectively tackling 3D problems.

What is the first step in solving a 3D problem according to the video?

• Estimate the dimensions visually

• Break it down into 2D components

• Calculate all angles first

• Use the cosine rule immediately

In the example of finding length CD, what is the first triangle used to calculate?

• The diagonal of the base

• The height of the cuboid

• The angle at the top

• The width of the cuboid

What is the calculated length of the diagonal across the base of the cuboid?

• sqrt 50

• sqrt 450

• sqrt 89

• sqrt 73

How is the height of the square-based pyramid determined?

• By using the cosine rule

• By measuring directly from the model

• By calculating the diagonal of the base and using Pythagoras' theorem

• By using the sine rule

What is the final calculated height of the square-based pyramid?

• 21.21 cm

• 23.74 cm

• 26 cm

• 15 cm

Which trigonometric function is used to calculate the angle that edge EB makes with the base?

• Secant

• Cosine

• Sine

• Tangent

What is the calculated angle that edge EB makes with the base?

• 30.0 degrees

• 65.9 degrees

• 90.0 degrees

• 45.0 degrees