Exploring Special Right Triangles and Trigonometry Concepts

This video tutorial covers the basics of trigonometry, focusing on the Pythagorean theorem and special right triangles, including 30-60-90 and 45-45-90 triangles. It provides practice problems to apply these concepts and introduces trigonometric ratios such as sine, cosine, and tangent. The tutorial also explores solving right triangles using these ratios and discusses trigonometric identities and patterns.

What is the formula for the Pythagorean theorem?

• a^2 - b^2 = c^2

• 2a + 2b = c^2

• a^2 + b^2 = c^2

• a^2 + b^2 = 2c

Which set of numbers is a Pythagorean triple?

• 3, 4, 5

• 2, 3, 4

• 6, 8, 9

• 5, 7, 8

In a 30-60-90 triangle, if the side opposite the 30° angle is 4, what is the length of the hypotenuse?

• 8

• 16

• 4√3

• 4√2

What is the length of the hypotenuse in a 45-45-90 triangle if one leg is 7?

• 14

• 7√3

• 49

• 7√2

In a 30-60-90 triangle, if the side opposite the 60° angle is 4√3, what is the length of the side opposite the 30° angle?

• 4

• 8

• 12

• 16

If the sine of an angle is 0.8, what is the cosecant of that angle?

• 4/5

• 0.8

• 5/4

• 1.25

What is the sine of 30 degrees?

• 1/√2

• √3/2

• √2/2

• 1/2

If the tangent of an angle is 1, what is the measure of the angle in a right triangle?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

What is the secant of 45 degrees?

• 1

• √3

• 2

• √2

What is the cosine of 60 degrees?

• 1/2

• 1/√2

• √2/2

• √3/2