30-60-90 Triangle Problems

The video tutorial covers solving word problems involving special right triangles, specifically 45-45-90 and 30-60-90 triangles. It includes three problems: calculating the side length of a square from its diagonal, determining the radius of the largest circle that can be cut from a square, and finding the height of a hexagonal shape made from equilateral triangles. Each problem is solved using proportions and the properties of special right triangles.

What are the two types of special right triangles discussed in the video?

• 30-30-60 and 45-45-90

• 45-45-90 and 60-60-60

• 30-60-90 and 60-60-60

• 30-60-90 and 45-45-90

In a 45-45-90 triangle, what is the ratio of the sides?

• 1:1:√2

• 1:1:1

• 1:√3:2

• 1:2:√3

If a square has a diagonal of 11 cm, what is the length of each side to the nearest tenth?

• 7.8 cm

• 10.0 cm

• 8.5 cm

• 9.0 cm

What type of triangle is formed by the diagonal of a square?

• Scalene triangle

• Acute triangle

• Equilateral triangle

• Isosceles right triangle

How do you calculate the side length of a square if you know the diagonal length?

• Multiply the diagonal by 2

• Divide the diagonal by 2

• Multiply the diagonal by √2

• Divide the diagonal by √2

What is the diameter of the largest circle that can be cut from a square with a diagonal of 14 cm?

• 12.0 cm

• 10.5 cm

• 11.0 cm

• 9.9 cm

What is the radius of the largest circle that can be cut from a square with a diagonal of 14 cm?

• 7.0 cm

• 6.0 cm

• 5.5 cm

• 4.9 cm

In a 30-60-90 triangle, what is the ratio of the sides?

• 1:2:√3

• 1:√3:2

• 1:1:1

• 1:1:√2

What is the length of the side of a square if its diagonal is 14 cm?

• 9.9 cm

• 10.5 cm

• 11.0 cm

• 12.0 cm

What is the height of a hexagonal shape formed by equilateral triangles with side length 7 cm?

• 8.08 cm

• 10.10 cm

• 14.14 cm

• 12.12 cm