Trigonometric Ratios and Hypotenuse

The video tutorial explains how to solve problems involving trigonometric ratios. It begins with identifying the appropriate trig ratio, setting up the equation with the given angle and sides, and using a calculator to convert the trig ratio into a decimal. The tutorial then demonstrates solving the equation using cross multiplication to find the unknown side, ensuring the hypotenuse is the longest side. An additional example is provided for further practice.

What is the first step in solving a trigonometric ratio problem?

• Use a calculator to find the decimal value.

• Identify the trigonometric ratio to use.

• Set up the equation with the given sides.

• Cross multiply to solve the equation.

Which trigonometric function is used when you have the opposite side and the hypotenuse?

• Tangent

• Cosine

• Sine

• Secant

If the reference angle is 50 degrees and the opposite side is 5, how do you set up the equation?

• sin(50) = 5/x

• tan(50) = x/5

• sec(50) = x/5

• cos(50) = 5/x

What is the decimal value of sin(50) rounded to four decimal places?

• 0.6428

• 0.7660

• 0.8660

• 0.5000

How do you set up a proportion using the decimal value of a trigonometric function?

• Multiply the decimal by the hypotenuse.

• Place the decimal over 1 and set it equal to the ratio of the sides.

• Add the decimal to the opposite side.

• Subtract the decimal from the hypotenuse.

What is the next step after setting up the proportion with the trigonometric ratio?

• Divide the sides by the decimal.

• Add the sides together.

• Subtract the opposite side from the hypotenuse.

• Cross multiply to solve for the unknown.

What is the length of the hypotenuse if the opposite side is 5 and sin(50) = 0.7660?

• 5.000

• 4.500

• 7.000

• 6.527

Why is it important to verify the length of the hypotenuse?

• To check if it is equal to the opposite side.

• To confirm it is longer than the opposite side.

• To make sure it is less than the adjacent side.

• To ensure it is the shortest side.

What should you do if the calculated hypotenuse does not seem correct?

• Ignore the result and move on.

• Use a different calculator.

• Check the angle and side values used.

• Recalculate using a different trigonometric function.

What is the significance of the hypotenuse in a right triangle?

• It is equal to the opposite side.

• It is always the longest side.

• It is always the shortest side.

• It is equal to the adjacent side.