Dolores is standing on a horizontal ground level with the base of the Statue of Liberty in New York City. The angle formed by the ground and the line segment from her position to the top of the statue is 26.3°. The height of the Statue of Liberty is approximately 93 meters. Find her distance from the Statue of Liberty to the nearest meter.
the distance from the Statue of Liberty to the nearest meter is210
You found the distance from Dolores to the top of the statue.
is that what you wanted, or the distance to the foot of the statue?
To find Dolores' distance from the Statue of Liberty, we can use trigonometry and the given information. Let's break down the problem into two right triangles: one formed by Dolores, the ground, and the line segment to the top of the statue, and another formed by the ground, the height of the statue, and the line segment from Dolores to the base of the statue.
Let's label the distance from Dolores to the base of the statue as x (the value we need to find).
Using trigonometry, we can use the tangent function to relate the angles and sides of a right triangle:
tan(26.3°) = height of the statue / x
First, we need to find the height of the statue in meters, which is given as approximately 93 meters.
tan(26.3°) = 93 / x
To solve for x, we can rearrange the equation:
x = 93 / tan(26.3°)
Using a scientific calculator, we can calculate the value of tan(26.3°) as approximately 0.4939.
x = 93 / 0.4939
x ≈ 187.98
Therefore, Dolores is approximately 188 meters away from the Statue of Liberty.