Q1. How high did you travel in the hot air balloon if your friend is 100 feet away and the angle of elevation is 31°?

Background

Topic: Right Triangle Trigonometry (Angle of Elevation)

This question tests your ability to use trigonometric ratios (specifically tangent) to solve for the height of an object when given a horizontal distance and an angle of elevation.

Key Terms and Formulas

• Angle of Elevation: The angle formed by the line of sight above the horizontal when looking up at an object.

• Opposite Side: The side opposite the angle of elevation (in this case, the height you traveled).

• Adjacent Side: The side next to the angle of elevation (the horizontal distance from your friend to the balloon).

• Tangent Ratio:

Step-by-Step Guidance

1. Draw and label a right triangle where the horizontal distance (adjacent side) is 100 ft, the angle of elevation is , and the height (opposite side) is what you need to find.

2. Write the tangent ratio for the angle of elevation:

3. Rearrange the equation to solve for the height:

4. Calculate using a calculator (make sure it is in degree mode).

5. Multiply the result by 100 to find the height you traveled.

Try solving on your own before revealing the answer!