Pythagorean Theorem and Triangle Dimensions

The video tutorial explains how to determine the dimensions of a park shaped as a right triangle. It covers the application of the Pythagorean Theorem and trigonometric ratios to solve for unknown side lengths. The problem involves a park with a known side along Euclid Avenue and a 50-degree angle. The tutorial demonstrates using the tangent ratio to find the length along Parallel Road and the Pythagorean Theorem to calculate the hypotenuse. The solution concludes with the approximate lengths of the park's sides.

What shape is the park that the local parks department wants to build?

• Circle

• Right Triangle

• Rectangle

• Square

What is the angle between Euclid Avenue and the side along Parallel Road?

• 45 degrees

• 60 degrees

• 50 degrees

• 30 degrees

What is the length of the side along Euclid Avenue?

• 10 yards

• 8 yards

• 12 yards

• 14 yards

What is the Pythagorean Theorem used for in right triangles?

• To calculate the perimeter of a triangle

• To relate the lengths of the sides of a right triangle

• To find the sum of angles in a triangle

• To find the area of a triangle

Which trigonometric ratio is used to find the length of the side along Parallel Road?

• Secant

• Tangent

• Cosine

• Sine

What is the approximate length of the side along Parallel Road?

• 20 yards

• 18 yards

• 16 yards

• 10 yards

What equation is used to find the hypotenuse of the triangle?

• x = y * z

• x^2 = y^2 - z^2

• x^2 = y^2 + z^2

• x = y + z

What is the approximate length of the hypotenuse of the park?

• 16 yards

• 18.9 yards

• 20 yards

• 22 yards

Which method is best for finding the hypotenuse when two legs of a right triangle are known?

• Using the tangent ratio

• Using the Pythagorean Theorem

• Using the cosine ratio

• Using the sine ratio

What is the final conclusion about the dimensions of the park?

• The park is a square with sides of 10 yards.

• The park is a rectangle with sides of 16 and 18.9 yards.

• The park is a right triangle with sides of 10, 16, and 18.9 yards.

• The park is a circle with a radius of 10 yards.