Finding the Hypotenuse Using Sine

The video tutorial explains how to find the length of the hypotenuse in a right triangle using the sine function. It begins by identifying the sides of the triangle relative to a given angle, then applies the sine function to set up an equation. The tutorial demonstrates solving the equation for the hypotenuse and using a calculator to find a decimal approximation, rounding to the nearest hundredth.

What is the main goal of the problem discussed in the video?

• To find the area of the triangle

• To find the length of the hypotenuse

• To find the measure of the angle

• To find the length of the adjacent side

Which side is opposite the given angle of 27 degrees?

• The side with an unknown length

• The side with a length of four units

• The side opposite the right angle

• The side with a length of x units

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

• Secant

• Sine

• Cosine

• Tangent

What is the equation set up to find the hypotenuse using the sine function?

• sine 27 degrees = x / 4

• sine 27 degrees = 4 / x

• sine 27 degrees = x / adjacent

• sine 27 degrees = adjacent / x

What is the first step in solving the equation for x?

• Divide both sides by 4

• Add x to both sides

• Subtract 4 from both sides

• Multiply both sides by x

How do you simplify the equation after multiplying both sides by x?

• Add sine 27 degrees

• Subtract x

• Divide by sine 27 degrees

• Multiply by 4

What is the final expression for x before using the calculator?

• x = 4 / sine 27 degrees

• x = 4 * sine 27 degrees

• x = 4 + sine 27 degrees

• x = sine 27 degrees / 4

What mode should the calculator be in to find the decimal approximation of x?

• Radian mode

• Degree mode

• Scientific mode

• Fraction mode

What is the approximate value of x rounded to the nearest hundredth?

• 8.91 units

• 8.61 units

• 8.81 units

• 8.71 units

Why do we round down the value of x in this problem?

• Because the third decimal place is a zero

• Because the third decimal place is a one

• Because the third decimal place is a five

• Because the third decimal place is a nine