Trigonometric Ratios in Right Triangles

This video tutorial explains how to find the sine value of an acute angle in a right triangle by using the properties of similar triangles. It reviews the basic properties of right triangles, including the hypotenuse and the relationship between angles and sides. The tutorial also covers how to identify the adjacent, opposite, and hypotenuse sides relative to a reference angle. It demonstrates calculating sine values using side length ratios, with examples for 30 and 60 degrees. The video concludes by noting that trigonometric ratios apply to all triangles, with further exploration in future lessons.

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

• The sum of all angles in the triangle

• The ratio of the adjacent leg to the opposite leg

• The ratio of the opposite leg to the hypotenuse

• The ratio of the hypotenuse to the adjacent leg

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

• Medium-sized side

• Opposite leg

• Adjacent leg

• Hypotenuse

In a right triangle, what is the relationship between the smallest angle and the sides?

• It is opposite the longest side

• It is opposite the shortest side

• It is opposite the medium-sized side

• It is adjacent to the hypotenuse

When using angle A as a reference, which side is the adjacent leg?

• Side AC

• Side BC

• Side CB

• Side AB

How can you avoid confusing the adjacent leg with the hypotenuse?

• Identify the longest side first

• Identify the side opposite the right angle first

• Identify the shortest side first

• Identify the side adjacent to the smallest angle first

What is the sine of 30 degrees in a right triangle?

• 1

• 1/2

• Square root of 3 over 2

• 2

What is the sine of 60 degrees in a right triangle?

• 1

• 1/2

• Square root of 3 over 2

• 2

Why are sine values invariant in similar triangles?

• Because the triangles have different areas

• Because the angles are different

• Because the side length ratios are the same

• Because the hypotenuse is always the longest side

Do trigonometric ratios like sine only apply to right triangles?

• Yes, but only in equilateral triangles

• No, they apply only to isosceles triangles

• No, they apply to any triangle

• Yes, only to right triangles

What will be covered in another lesson regarding trigonometric ratios?

• Their application in non-right triangles

• Their application in polygons

• Their application in quadrilaterals

• Their application in circles