Trigonometry and Balloon Height Calculations

This video tutorial demonstrates how to find the height of a balloon using basic trigonometry. The problem involves measuring a horizontal distance of 2,000 feet and an angle of 30° to the balloon. The tutorial explains how to set up and solve a trigonometric equation using the tangent function to find the height. The final calculation shows the balloon's height to be approximately 1,154 feet.

What is the main objective of the video tutorial?

• To determine the weight of a balloon.

• To measure the speed of a balloon.

• To find the height of a balloon using trigonometry.

• To calculate the distance to a balloon.

What is the horizontal distance from the observer to the balloon?

• 1,000 ft

• 4,000 ft

• 2,000 ft

• 3,000 ft

What angle is measured from the observer to the balloon?

• 60°

• 45°

• 30°

• 15°

Which trigonometric function is used to relate the opposite and adjacent sides in this problem?

• Cosine

• Sine

• Tangent

• Cotangent

What does the tangent of an angle represent in trigonometry?

• The ratio of the opposite side to the hypotenuse

• The ratio of the hypotenuse to the adjacent side

• The ratio of the opposite side to the adjacent side

• The ratio of the adjacent side to the hypotenuse

What is the variable used to represent the height of the balloon?

• X

• Y

• O

• Z

What is the first step in isolating the variable Y in the equation?

• Add 2,000 to both sides

• Subtract 2,000 from both sides

• Divide both sides by 2,000

• Multiply both sides by 2,000

What should you ensure about your calculator before calculating the tangent of 30°?

• It is in radian mode

• It is in degree mode

• It is in scientific mode

• It is in standard mode

What is the approximate value of the tangent of 30° used in the calculation?

• 0.577

• 1.732

• 0.866

• 0.5

What is the final calculated height of the balloon?

• 1,000 ft

• 2,000 ft

• 1,154 ft

• 1,500 ft