Trigonometric Ratios and Right Triangles

This video tutorial introduces trigonometry in right triangles, focusing on the SOH CAH TOA mnemonic to solve problems. It provides examples using 30 and 60-degree angles and applies these concepts to a real-world problem involving a building. The tutorial emphasizes understanding the relationships between angles and sides in right triangles.

What does the mnemonic SOH CAH TOA help you remember in trigonometry?

• The order of operations

• The types of triangles

• The trigonometric ratios

• The Pythagorean theorem

In a right triangle, if angle X is your reference, which side is the opposite?

• The longest side

• The hypotenuse

• The side opposite to angle X

• The side adjacent to angle X

Using SOH CAH TOA, how do you calculate the sine of a 30-degree angle?

• Adjacent over hypotenuse

• Opposite over adjacent

• Hypotenuse over opposite

• Opposite over hypotenuse

If the sine of 30 degrees is 0.5, what is the length of the opposite side if the hypotenuse is 12 cm?

• 3 cm

• 12 cm

• 6 cm

• 9 cm

What is the tangent of a 60-degree angle in a right triangle?

• 1

• √3

• 1/2

• √3/2

In a triangle with a 60-degree angle, if the adjacent side is 15 cm, what is the hypotenuse using cosine?

• 15 cm

• 30 cm

• 20 cm

• 25 cm

In a right triangle, if the angle is 60 degrees and the opposite side is 15√3 cm, what is the length of the adjacent side?

• 15 cm

• 25 cm

• 20 cm

• 30 cm

How do you determine the length of the adjacent side using cosine in a right triangle with a 60-degree angle?

• Multiply the hypotenuse by the sine of 60

• Multiply the hypotenuse by the cosine of 60

• Divide the hypotenuse by the sine of 60

• Divide the hypotenuse by the cosine of 60

In a contextual problem, if an observer sees the top of a building at a 30-degree angle and then at a 60-degree angle after moving 50 meters closer, what is the height of the building?

• 25 meters

• 50√3 meters

• 50 meters

• 25√3 meters

What is the distance from the observer to the building if the angle of elevation changes from 30 to 60 degrees after moving 50 meters closer?

• 100 meters

• 75 meters

• 25 meters

• 50 meters