Finding Missing Side Lengths with Trig Ratios

The video tutorial explains how to solve trigonometric problems by identifying the appropriate trig function to use. It covers the use of tangent to find a missing side when given an angle and one side, and the use of sine to find the hypotenuse when given an angle and the opposite side. The tutorial emphasizes logical reasoning and the use of calculators for accurate results.

Which trigonometry function is used to find a missing side when given an angle and the length of another side?

• Tangent

• Cosine

• Sine

• Cotangent

What does SOHCAHTOA stand for?

• Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent

• Sine = Hypotenuse/Opposite, Cosine = Opposite/Adjacent, Tangent = Hypotenuse/Adjacent

• Sine = Opposite/Adjacent, Cosine = Hypotenuse/Adjacent, Tangent = Opposite/Hypotenuse

• Sine = Adjacent/Opposite, Cosine = Hypotenuse/Opposite, Tangent = Adjacent/Hypotenuse

How do you calculate the length of a side using the tangent function?

• Multiply the length of the given side by the tangent of the given angle

• Divide the length of the given side by the tangent of the given angle

• Add the length of the given side to the tangent of the given angle

• Subtract the tangent of the given angle from the length of the given side

What is the result when the tangent of 12 degrees is multiplied by 4?

• 1.2

• 3.6

• 2.4

• 0.85

Why does a smaller angle in a right triangle result in a shorter opposite side when the adjacent side's length is fixed?

• Because the cosine of the angle increases

• Because the hypotenuse decreases

• Because the sine of the angle decreases

• Because the tangent of the angle decreases

Which function is used to find the hypotenuse when given an angle and the length of the opposite side?

• Sine

• Cosine

• Tangent

• Secant

How do you solve for the hypotenuse when the variable is in the denominator of the sine function?

• Subtract the sine of the given angle from both sides

• Add the sine of the given angle to both sides

• Divide both sides by the sine of the given angle

• Multiply both sides by the sine of the given angle

What is the length of the hypotenuse when the opposite side is 18 and the angle is 72 degrees?

• 18.9

• 17.5

• 19.2

• 20.1

Why must the hypotenuse be longer than the other sides in a right triangle?

• Because it is the sum of the other two sides

• Because it is always the longest side by definition

• Because it is opposite the largest angle

• Because it is opposite the smallest angle

What logical reasoning confirms the calculated length of the hypotenuse in the second problem?

• The hypotenuse is equal to the opposite side

• The hypotenuse is shorter than the opposite side

• The hypotenuse is twice the length of the opposite side

• The hypotenuse is longer than the opposite side