Trigonometric Ratios and Applications

In this video, the teacher reviews trigonometric ratios and demonstrates how to find unknown side lengths in right-angle triangles using sine and tangent ratios. The video begins with identifying triangle sides and progresses to solving equations to find unknown lengths. A practice problem is provided for students to apply the tangent ratio. The video concludes with a summary and a preview of the next topic.

What is the primary focus of the video?

• Calculating areas of triangles

• Using known side lengths to find trigonometric ratios

• Finding angles using trigonometric ratios

• Understanding the Pythagorean theorem

What is the first step in solving for an unknown side using trigonometric ratios?

• Using a calculator to find the ratio

• Identifying the opposite, adjacent, and hypotenuse

• Calculating the area of the triangle

• Finding the angle of interest

If the sine of an angle is 1/3, what does this ratio represent?

• The ratio of the opposite side to the adjacent side

• The ratio of the opposite side to the hypotenuse

• The ratio of the hypotenuse to the opposite side

• The ratio of the adjacent side to the hypotenuse

In the example given, what is the length of the hypotenuse?

• 16 cm

• 8 cm

• 12 cm

• 24 cm

What is the value of X when the sine of the angle is 1/3 and the hypotenuse is 24?

• 10

• 12

• 8

• 6

What is the tangent of an angle defined as?

• The ratio of the opposite side to the hypotenuse

• The ratio of the adjacent side to the hypotenuse

• The ratio of the opposite side to the adjacent side

• The ratio of the hypotenuse to the opposite side

In the tangent example, what is the length of the adjacent side?

• 24

• 13

• 26

• 12

What is the value of X when the tangent of the angle is 1/2 and the adjacent side is 26?

• 13

• 12

• 24

• 26

What is the final step in solving for an unknown side using a trigonometric ratio?

• Identifying the hypotenuse

• Setting up an equation and solving it

• Finding the angle of interest

• Using a calculator to find the ratio

What is the purpose of multiplying both sides of the equation by 26 in the tangent example?

• To eliminate the hypotenuse

• To solve for the angle

• To find the length of the hypotenuse

• To isolate the variable X