3D Trigonometry: Solving for the Angle between a Line and a Plane in a Triangular Prism

The video tutorial explains how to solve a geometry problem involving a 3D shape. It begins by identifying the problem and the given data, then proceeds to set up the problem by identifying relevant triangles. The tutorial applies Pythagoras' theorem to find side lengths and uses trigonometry to calculate the angle between a line and a plane. The solution is summarized with a focus on the methods used and the allocation of marks for each step.

What is the task in this problem involving line BE and plane ABCD?

• Determine the area of plane ABCD.

• Calculate the length of line BE.

• Identify the midpoint of line BE.

• Find the angle between line BE and plane ABCD.

Which triangle is formed to help find the angle between line BE and plane ABCD?

• Triangle CDE

• Triangle ABD

• Triangle ABE

• Triangle DBE

What is the length of side AD in triangle ADB?

• 8 cm

• 16 cm

• 24 cm

• 10 cm

Which theorem is used to find the length of side DB in triangle ADB?

• Pythagoras' Theorem

• Sine Rule

• Area Theorem

• Cosine Rule

What is the calculated length of side DB in terms of square roots?

• 16√5

• 24√2

• 10√8

• 8√10

Which trigonometric function is used to find angle X in triangle DBE?

• Secant

• Tangent

• Cosine

• Sine

What is the formula for tangent in terms of opposite and adjacent sides?

• Tangent = Adjacent / Opposite

• Tangent = Opposite / Adjacent

• Tangent = Adjacent / Hypotenuse

• Tangent = Opposite / Hypotenuse

What is the value of angle X rounded to one decimal place?

• 22.0 degrees

• 21.6 degrees

• 21.5 degrees

• 20.5 degrees

How many marks are allocated for using Pythagoras' theorem in this problem?

• One mark

• Two marks

• Three marks

• Four marks

What is the importance of knowing the formulae like SOHCAHTOA and Pythagoras' theorem?

• They are used to calculate areas of circles.

• They are essential for solving geometry problems.

• They help in solving complex algebra problems.

• They are provided in the exam.