A flagpole cast a 20-foot shadow on the ground perpendicular to its base. The angle of elevation from the end of the shadow to the top of the flagpole is 30°. Which measurement is closest to the height, in feet, of the flagpole? *
To solve this problem, we can use trigonometry.
Let's call the height of the flagpole "h."
First, let's find the length of the base of the triangle formed by the shadow and the height of the flagpole. We know that the length of the shadow is 20 feet.
Next, let's find the length of the opposite side of the triangle, which is the height of the flagpole.
We can use the tangent function since we have the opposite and adjacent sides.
tan(30°) = h / 20
To find h, we can rearrange the equation:
h = 20 * tan(30°)
Using a calculator, we can find the value of tan(30°) ≈ 0.577
Now, let's calculate h:
h = 20 * 0.577 ≈ 11.54
Therefore, the measurement closest to the height of the flagpole is approximately 11.54 feet.
To solve this problem, we can use the concept of trigonometry. Let's break it down step by step:
1. Draw a diagram: Draw a vertical line to represent the flagpole. Label its height with 'h'. Draw a horizontal line to represent the ground. Label the length of the shadow with '20'.
2. Identify the right triangle: From the end of the shadow to the top of the flagpole, we have a right triangle. The angle of elevation, which is the angle between the flagpole and the line of sight from the end of the shadow to the top of the flagpole, is given as 30°.
3. Identify the trigonometric ratio: In a right triangle, the tangent ratio is defined as the ratio of the opposite side to the adjacent side. In this case, the height of the flagpole ('h') is the opposite side, and the length of the shadow ('20') is the adjacent side.
4. Use the tangent ratio: The tangent of an angle can be found by dividing the opposite side by the adjacent side. In this case, we have the equation tan(30°) = h/20.
5. Solve for the height: Rearrange the equation to isolate 'h'. Multiply both sides of the equation by 20, giving us 20 * tan(30°) = h.
6. Calculate the height: Use a calculator to find the tangent of 30°, which is approximately 0.5774. Multiply this value by 20 to get the height: h ≈ 11.548 feet.
Therefore, the height of the flagpole is closest to 11.548 feet.
After you make your sketch, you will see that
tan 30° = h/20
h = 20tan30° = ...... ft