Geometry Problems and Concepts

This video tutorial demonstrates the application of Pythagoras' theorem to solve various real-world problems. It covers calculating the diagonal of a TV screen, determining the length of a footpath, finding the slope length of an aircraft hanger roof, and calculating unknown boundary dimensions in a subdivision. Each problem involves identifying right angle triangles and using Pythagoras' theorem to find unknown lengths.

What is the first step in applying Pythagoras' theorem to solve real-world problems?

• Measure all sides of the triangle

• Convert all measurements to meters

• Identify a right-angle triangle

• Calculate the area of the triangle

How is the size of a TV typically measured?

• By its screen area

• By its diagonal length

• By its height

• By its width

If a TV has a width of 135 cm and a height of 75 cm, what is the diagonal length?

• 154 cm

• 165 cm

• 150 cm

• 160 cm

In the road plan problem, what is the angle between the footpath and the road at point Y?

• 120°

• 60°

• 45°

• 90°

What is the length of the footpath connecting points X and Y in the road plan?

• 42 m

• 60 m

• 53 m

• 32 m

What shape does the roof of the aircraft hangar form?

• Scalene triangle

• Equilateral triangle

• Right triangle

• Isosceles triangle

What is the calculated length of the sloping roof of the aircraft hangar?

• 33.5 m

• 30.5 m

• 32.0 m

• 31.2 m

How is the quadrilateral boundary divided to calculate the unknown dimension?

• Into two squares

• Into two rectangles

• Into two right-angle triangles

• Into two circles

What is the length of the diagonal in the top triangle of the quadrilateral boundary?

• 150 m

• 155 m

• 165 m

• 161 m

What is the unknown boundary dimension X in the quadrilateral problem?

• 72 m

• 70 m

• 68 m

• 65 m