Height and Properties of Triangles

The video tutorial explains how to find the height of a figure formed by circles arranged in a triangular pattern. It begins by discussing why the height is not simply three times the diameter of the circles. The tutorial then plots the centers of the circles to form an equilateral triangle and uses the Pythagorean theorem to calculate the height of the triangle. Alternative methods using trigonometry are also explored to verify the height calculation. The final height of the figure is determined to be approximately 27.32 cm.

What is the initial incorrect assumption about the height of the figure formed by circles?

• It is twice the radius of a circle.

• It is three times the diameter of a circle.

• It is equal to the circumference of a circle.

• It is half the diameter of a circle.

What shape is formed by the centers of the circles?

• Scalene triangle

• Isosceles triangle

• Right triangle

• Equilateral triangle

What is the length of each side of the equilateral triangle formed by the circle centers?

• 25 cm

• 20 cm

• 10 cm

• 15 cm

Which theorem is used to calculate the height of the equilateral triangle?

• Pythagorean theorem

• Sine rule

• Cosine rule

• Area theorem

What is the length of the leg of the right triangle formed within the equilateral triangle?

• 10 cm

• 5 cm

• 15 cm

• 20 cm

Which trigonometric function is used to find the height of the triangle?

• Cotangent

• Tangent

• Cosine

• Sine

What is the sine of a 60° angle in a 30-60-90 triangle?

• 1

• √2/2

• √3/2

• 1/2

What is the height of the triangle in terms of x?

• x + 10

• x + 5

• x + 20

• x + 15

What is the exact height of the entire figure?

• 20 cm

• 25 cm

• 30 cm

• 10√3 + 10 cm

What is the approximate decimal height of the entire figure?

• 28.5 cm

• 27.32 cm

• 25.5 cm

• 26.8 cm