Trigonometric Ratios in Right Triangles

The video tutorial covers the calculation of sine, cosine, and tangent for acute angles in right triangles. It begins with an introduction to the concepts and progresses to using the Pythagorean theorem to find missing side lengths. The tutorial then demonstrates how to calculate trigonometric ratios for specific angles in right triangles, including special 45-45-90 triangles. The instructor emphasizes the importance of recognizing special triangles to save time and explains the reasoning behind the trigonometric ratios.

What is the first step in finding the sine, cosine, and tangent of acute angles in a right triangle?

• Calculate the area of the triangle

• Measure the angles with a protractor

• Find the missing side using the Pythagorean theorem

• Identify the hypotenuse

According to the Pythagorean theorem, what does a^2 + b^2 equal?

• The product of the legs

• The sum of the angles

• The square of the hypotenuse

• The perimeter of the triangle

What is the sine of angle J if the opposite side is 6 and the hypotenuse is 2√10?

• 3√10/10

• 1/√10

• 6/2√10

• 3/√10

How do you rationalize the denominator of 3/√10?

• Multiply by 10

• Multiply by √10/√10

• Add 10

• Divide by 3

What is the cosine of angle J if the adjacent side is 2 and the hypotenuse is 2√10?

• √10/10

• 2√10/10

• 2/√10

• 1/√10

What is the tangent of angle J if the opposite side is 6 and the adjacent side is 2?

• 2

• 3

• 6

• 1/3

What is the sine of angle K if the opposite side is 2 and the hypotenuse is 2√10?

• 2/√10

• √10/10

• 2√10/10

• 1/√10

What is the cosine of angle K if the adjacent side is 6 and the hypotenuse is 2√10?

• 6/√10

• 3/√10

• 3√10/10

• 6√10/10

What is the tangent of angle K if the opposite side is 2 and the adjacent side is 6?

• 6

• 2/3

• 1/3

• 3

What is a characteristic of a 45-45-90 triangle?

• The hypotenuse is equal to one leg

• One angle is 60 degrees

• The legs are equal in length

• The hypotenuse is twice the length of one leg