If you are standing 85 ft from the base of a flagpole, and determine that at ground level, you would need to look up at a 30° angle to see the top of the flagpole, how tall is the flagpole? Round the height to tenths.
h/85 = tan 30° = 1/√3
h = 85/√3 = 49.1 ft
3x+7=-2x-8
To find the height of the flagpole, we can use trigonometry. Let's consider the situation:
1. The distance from the base of the flagpole to your position is 85 ft.
2. The angle of elevation from your position to the top of the flagpole is 30°.
We can use the tangent function to find the height of the flagpole. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the flagpole (h), and the adjacent side is the distance from the base of the flagpole to your position (85 ft).
So, the equation becomes:
tan(30°) = h/85
Now, let's solve for h:
h = tan(30°) * 85
Using a calculator, we find that tan(30°) is approximately 0.577.
h ≈ 0.577 * 85
h ≈ 49.045 ft
Therefore, the height of the flagpole is approximately 49.0 ft.
To determine the height of the flagpole, we can use trigonometry. First, let's draw a right triangle representing the situation. The base of the triangle will be the distance from you to the base of the flagpole (85 ft), and the vertical leg will be the height of the flagpole. The angle between the ground and your line of sight (30°) will be the angle opposite the vertical leg of the triangle.
Now, we can use the tangent function (tan) to find the height of the flagpole. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle. In this case, we have the opposite side (height) and want to solve for it.
The formula for tangent is:
tan(angle) = opposite / adjacent
Plugging in the given values:
tan(30°) = height / 85 ft
To solve for the height, we can multiply both sides of the equation by 85 ft:
85 ft * tan(30°) = height
Using a scientific calculator or a trigonometric table, we can find the tangent of 30 degrees, which is approximately 0.5773. Multiplying this by 85 ft, we get:
85 ft * 0.5773 ≈ 49.1 ft
Therefore, the height of the flagpole is approximately 49.1 feet (rounded to tenths).