Trigonometric Relationships in Triangles

The video tutorial explains how to determine the length of a side labeled X in a geometric problem involving two right triangles. The problem is set up by identifying the angles and given lengths. Variables X and Y are defined, and two trigonometric equations are established. These equations are solved as a system to find the values of X and Y. Approximations for tangent values are used to simplify calculations. The final result is that X is approximately 2,776 feet.

What is the measure of the angle labeled 32 degrees in the problem?

• An acute angle

• A right angle

• A straight angle

• An obtuse angle

How many right triangles are identified in the problem setup?

• Three

• Four

• Two

• One

What variable is used to represent the unknown side in the smaller triangle?

• Z

• Y

• W

• X

Which trigonometric function is used to relate X and Y in the smaller triangle?

• Cosine

• Cotangent

• Sine

• Tangent

What is the equation derived from the larger triangle involving X and Y?

• X = tangent 26 degrees * (Y + 1,250)

• X = Y * tangent 32 degrees

• X = Y / tangent 26 degrees

• X = Y + 1,250

What is the approximate value of tangent 32 degrees used in the calculations?

• 0.8391

• 0.4877

• 0.6249

• 0.7321

What is the result of the calculation 0.4877 * 1,250?

• 500.125

• 800.425

• 700.325

• 609.625

What is the approximate value of Y after solving the equation?

• 4,443.3

• 3,500.2

• 5,000.5

• 6,250.7

What operation is performed to find X after determining Y?

• Addition

• Subtraction

• Multiplication

• Division

What is the final rounded value of X to the nearest foot?

• 2,500 feet

• 2,776 feet

• 3,250 feet

• 3,000 feet