Right Triangle Properties and Trigonometric Ratios

The video tutorial covers right triangle trigonometry, focusing on the definitions of hypotenuse, adjacent, and opposite sides. It introduces the SOHCAHTOA acronym to help remember sine, cosine, and tangent ratios. The tutorial includes example problems to demonstrate how to calculate these ratios and solve for unknown sides using the Pythagorean theorem. Advanced problems are also discussed, and the session concludes with homework instructions.

What is the primary focus of trigonometry?

• Study of polygons

• Study of circles

• Study of triangles

• Study of squares

Which side is always opposite the right angle in a right triangle?

• Hypotenuse

• Base

• Adjacent side

• Opposite side

In a right triangle, which side is adjacent to angle Theta?

• The longest side

• The side next to Theta

• The hypotenuse

• The side opposite Theta

What is the sine of an angle in a right triangle?

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite

What is the cosine of an angle in a right triangle?

• Opposite over adjacent

• Opposite over hypotenuse

• Hypotenuse over adjacent

• Adjacent over hypotenuse

What is the tangent of an angle in a right triangle?

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite

In a 30-60-90 triangle, what is the length of the side opposite the 30-degree angle if the hypotenuse is 2?

• √2

• 2

• √3

• 1

In a 45-45-90 triangle, what is the ratio of the legs to the hypotenuse?

• 1:1:√2

• 1:√3:2

• 1:2:√3

• 1:1:2

What theorem is used to find the length of a side in a right triangle when the other two sides are known?

• Cosine rule

• Sine rule

• Tangent rule

• Pythagorean theorem

If one leg of a right triangle is 3 and the hypotenuse is 5, what is the length of the other leg?

• 6

• 7

• 5

• 4