Trigonometric Functions and Right Triangles

This video tutorial explains how to find the length of the hypotenuse in a right triangle using the cosine function. It begins by identifying the sides of the triangle relative to a given angle, then applies the cosine function to set up an equation. The tutorial demonstrates solving the equation for the hypotenuse length, using a calculator to compute and round the result to the nearest hundredth. The process is explained step-by-step, ensuring clarity in understanding the application of trigonometry and algebra.

What is the angle given in the problem for the right triangle?

• 30 degrees

• 42 degrees

• 90 degrees

• 60 degrees

Which side of the triangle is opposite the right angle?

• Hypotenuse

• Base

• Adjacent side

• Opposite side

What is the length of the adjacent side in the given triangle?

• 20 units

• 15 units

• 11 units

• 5 units

Which trigonometric function is used to find the hypotenuse in this problem?

• Tangent

• Cosine

• Secant

• Sine

What is the formula for cosine in terms of the sides of a right triangle?

• Adjacent/Hypotenuse

• Opposite/Hypotenuse

• Adjacent/Opposite

• Hypotenuse/Adjacent

What operation is performed to clear the fraction in the equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the next step after multiplying both sides by x in the equation?

• Divide both sides by cosine 42 degrees

• Multiply both sides by cosine 42 degrees

• Add x to both sides

• Subtract x from both sides

What should you ensure before using the calculator for the final calculation?

• Calculator is in degree mode

• Calculator is in radian mode

• Calculator is in standard mode

• Calculator is in scientific mode

What is the approximate length of the hypotenuse rounded to the nearest hundredth?

• 13.50 units

• 14.80 units

• 16.00 units

• 15.20 units

Why do we round down the final answer in this problem?

• Because the units place is 0

• Because the tens place is 8

• Because the hundreds place is 5

• Because the thousands place is 1