Trigonometric Ratios and Triangle Properties

The video tutorial explains the concept of complementary angles using a 30-60-90 triangle, highlighting the relationships between sine, cosine, and tangent for angles 30 and 60 degrees. It then introduces the unique properties of 45-degree angles, demonstrating how they form isosceles right triangles and discussing the trigonometric ratios for these angles.

What is the complementary angle of 60 degrees in a right triangle?

• 30 degrees

• 45 degrees

• 90 degrees

• 60 degrees

Which trigonometric ratio is equal to sine 60 in a 30-60-90 triangle?

• sine 30

• cosine 60

• tangent 30

• cosine 30

What is the value of tangent 60 in a 30-60-90 triangle?

• 2

• 1

• √3

• 1/√3

What type of triangle is formed when an angle is its own complement?

• Equilateral

• Scalene

• Right

• Isosceles

Which angle in a triangle is its own complement?

• 30 degrees

• 45 degrees

• 90 degrees

• 60 degrees

In an isosceles right triangle, if one side is 1, what is the length of the hypotenuse?

• √3

• 2

• √2

• 1

What is the sine of a 45-degree angle in an isosceles right triangle?

• 1

• 1/√2

• √2

• 0

Why is sine 45 equal to cosine 45 in an isosceles right triangle?

• They are not equal

• 45 is its own complement

• Both are zero

• Both are one

What is the value of tangent 45 in an isosceles right triangle?

• 2

• 0

• √2

• 1

What is the cosine of a 45-degree angle in an isosceles right triangle?

• 0

• √2

• 1/√2

• 1