The Eiffel Tower is 300 m tall. When you are standing at a certain place in Paris, it subtends an angle of 7.0°. How far are you, then, from the Eiffel Tower?
To find the distance from the Eiffel Tower when it subtends an angle of 7.0°, we can use trigonometry.
Let's denote the distance from the Eiffel Tower as "x".
We can use the tangent function, which relates the angle and the opposite side (height of the tower) to the adjacent side (distance from the tower).
The formula for tangent is: tan(angle) = opposite/adjacent
In this case, tan(7.0°) = 300m / x
To find x, we can rearrange the formula as follows:
x = 300m / tan(7.0°)
Now, let's calculate the distance:
x ≈ 2493.85 m
Therefore, when standing at that certain place, you are approximately 2493.85 meters away from the Eiffel Tower.
To find the distance from the Eiffel Tower, we can use the concept of trigonometry. We can use the tangent function (tan) to calculate the distance.
Let's denote the distance from the Eiffel Tower as "x" (in meters).
We know the height of the Eiffel Tower is 300 meters, and when you are standing at a certain place in Paris, it subtends an angle of 7.0°. In a right triangle formed by the Eiffel Tower, the distance from the tower, and the angle subtended at your location, the tangent of the angle can be expressed as the ratio of the opposite side (height of the Eiffel Tower) to the adjacent side (distance from the Eiffel Tower):
tan(7.0°) = 300 / x
To find the value of x, we can rearrange the equation:
x = 300 / tan(7.0°)
Now, we can simply calculate x by taking the reciprocal of the tangent of 7.0° and multiplying it by 300:
x ≈ 300 / tan(7.0°)
Using a calculator, we find that tan(7.0°) is approximately 0.1227. Plugging this value into the equation:
x ≈ 300 / 0.1227
x ≈ 2444.63 meters
Therefore, when you are standing at a certain place in Paris and the Eiffel Tower subtends an angle of 7.0°, you are approximately 2444.63 meters away from the Eiffel Tower.