Trigonometric Ratios and Applications

This video tutorial covers the application of trigonometry in right triangles through three example problems. The first problem involves finding the value of X in a right triangle using trigonometric ratios. The second problem calculates the height at which an airplane passes over a hill, and the third problem determines the horizontal displacement of a person on a zipline. Each problem is solved step-by-step, demonstrating the use of sine, cosine, and tangent functions.

What is the first step to solve for x in the given right triangle problem?

• Find the hypotenuse of the smaller triangle.

• Identify the known sides and angles in the larger triangle.

• Use the Pythagorean theorem directly.

• Calculate the area of the triangle.

Which trigonometric ratio is used to find the unknown side y in the larger triangle?

• Cosine

• Tangent

• Sine

• Secant

What is the value of y when the hypotenuse is 40 and the angle is 30 degrees?

• 10

• 20

• 30

• 40

Which trigonometric ratio is used to find the value of x after finding y?

• Sine

• Cosine

• Tangent

• Cotangent

What is the value of x when the angle is 60 degrees and the opposite side is 20?

• 30

• 20

• 40

• 10

In the airplane problem, what is the distance from the runway to the hill?

• 5.8 km

• 4.8 km

• 3.8 km

• 2.8 km

What trigonometric ratio is used to find the height at which the airplane passes over the hill?

• Tangent

• Cotangent

• Cosine

• Sine

What is the height of the airplane above the hill if the angle of ascent is 15 degrees?

• 1.5 km

• 0.5 km

• 2.5 km

• 3.5 km

In the zipline problem, what is the height difference between the two ends of the cable?

• 46 m

• 42 m

• 48 m

• 44 m

What is the horizontal distance traveled by the person on the zipline?

• 200 m

• 150 m

• 250 m

• 300 m