Question

In a 6th graders response , What steps you would use to solve the following problem?


"You are standing 100 ft away from a veyr tall builidnd. Your line of sight is 6 ft from the ground. In f the angle of elevation (measured by a protractor) to the top of the building is 80 degrees, how tall is the building?"

Answer 1

To solve the problem of finding the height of the building, you can follow these steps:

1. **Understand the Problem**: You're standing 100 feet away from a very tall building, and your eye level is 6 feet from the ground. The angle you can see to the top of the building is 80 degrees.

2. **Draw a Diagram**: It helps to sketch a right triangle. Draw a horizontal line representing the ground, and mark where you stand (point A). From there, draw a vertical line straight up to represent the height of the building (point B). The angle from your eye level (the 6-foot mark) to the top of the building forms the angle of elevation (80 degrees). Label the height of the building above your eye level as "h."

3. **Identify the Triangle**: The right triangle consists of:
- The horizontal distance from you to the building (100 ft)
- The vertical distance from your eye level to the top of the building (h)
- The angle of elevation (80 degrees)

4. **Use Trigonometry**: Since we have a right triangle, we can use the tangent function, which relates the angle of elevation, the opposite side (the height above your eye level), and the adjacent side (the distance away from the building):
- Tan(angle) = opposite/adjacent
- Tan(80 degrees) = h / 100 ft

5. **Set Up the Equation**: With what we have, we can write the equation:
- Tan(80 degrees) = h / 100

6. **Solve for h**: To find h, you can rearrange the equation:
- h = 100 * Tan(80 degrees)

7. **Calculate Tan(80 degrees)**: You can use a calculator to find the tangent of 80 degrees. (Make sure your calculator is set to degrees, not radians.)
- Tan(80 degrees) is approximately 5.76 (this is just an example number, you should calculate it!)

8. **Find h**: Now plug that value back into the equation:
- h = 100 * 5.76 = 576 ft

9. **Add Your Eye Level Height**: Since h is the height above your eye level, you need to add that 6 ft to find the total height of the building:
- Total height = h + 6 ft = 576 ft + 6 ft = 582 ft

10. **Final Answer**: The height of the building is approximately 582 feet.

So, the steps to solve the problem are: draw a diagram, set up a right triangle, use the tangent function to find the height above your eye level, and then add your eye level height to get the total height of the building.