A person is standing 50 meters away from a vertical pole. If the angle of elevat
Practice Questions
Q1
A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?
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Questions & Step-by-Step Solutions
A person is standing 50 meters away from a vertical pole. If the angle of elevation of the top of the pole is 60 degrees, what is the height of the pole?
Step 1: Understand the problem. You have a pole and a person standing 50 meters away from it.
Step 2: The angle of elevation to the top of the pole is given as 60 degrees.
Step 3: Recall the tangent function in a right triangle: tan(angle) = opposite side / adjacent side.
Step 4: In this case, the opposite side is the height of the pole, and the adjacent side is the distance from the person to the pole (50 meters).
Step 5: Write the equation using the tangent of the angle: tan(60°) = height / 50.
Step 6: Find the value of tan(60°). It is equal to √3.
Step 7: Substitute tan(60°) into the equation: √3 = height / 50.
Step 8: To find the height, multiply both sides of the equation by 50: height = 50 * √3.
Step 10: The final height of the pole is approximately 86.6 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the pole and the distance from the pole.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the pole, the ground, and the line of sight.
