A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 30 degrees, what is the height of the pole?
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A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 30 degrees, what is the height of the pole?
Q: A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 30 degrees, what is the height of the pole?
Step 1: Understand the problem. You have a person standing 25 meters away from a vertical pole and looking up at the top of the pole at an angle of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the pole (which we want to find), the other side is the distance from the person to the pole (25 meters), and the angle between the ground and the line of sight to the top of the pole is 30 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole). So, tan(30 degrees) = height / 25 meters.
Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 5: Set up the equation. Now, we can write the equation: height = 25 * tan(30 degrees). This means height = 25 * (1/√3).
Step 6: Calculate the height. Multiply 25 by (1/√3) to find the height of the pole: height = 25/√3.
Step 7: Simplify the result. You can approximate 25/√3 to get about 12.5 meters.
