Trigonometric Functions and Equations

The video tutorial explains how to solve for the length of the adjacent side (x) in a right triangle using trigonometry. Given a right triangle with a 38-degree angle, an unknown opposite side, an adjacent side of length x, and a hypotenuse of length 12, the cosine function is used. The equation is set up as cosine 38 degrees equals x divided by 12. By multiplying both sides by 12, the exact value of x is found to be 12 times cosine 38 degrees. A calculator can be used to find the decimal approximation of x, which is approximately 9.456.

In the given right triangle, what is the length of the hypotenuse?

• 12

• 38 degrees

• Unknown

• x

Which trigonometric function is used to relate the adjacent side and the hypotenuse in this problem?

• Tangent

• Sine

• Secant

• Cosine

What is the equation used to solve for x in terms of cosine?

• cosine 38 degrees = 12 / x

• cosine 38 degrees = x / 12

• cosine 38 degrees = x * 12

• cosine 38 degrees = 12 * x

How do you solve for x once the equation is set up?

• Add 12 to both sides

• Multiply both sides by 12

• Divide both sides by 12

• Subtract 12 from both sides

What is the approximate decimal value of x?

• 10.123

• 9.456

• 8.789

• 11.234