From a point on the ground, the angle of elevation to the top of a 40-meter tall building is 60 degrees. How far is the point from the base of the building?
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Q1
From a point on the ground, the angle of elevation to the top of a 40-meter tall building is 60 degrees. How far is the point from the base of the building?
Q: From a point on the ground, the angle of elevation to the top of a 40-meter tall building is 60 degrees. How far is the point from the base of the building?
Step 1: Understand the problem. We have a building that is 40 meters tall, and we want to find out how far away we are from the base of the building when looking up at it at a 60-degree angle.
Step 2: Draw a right triangle. The height of the building is one side (40 meters), the distance from the point on the ground to the base of the building is the other side, and the line of sight to the top of the building is the hypotenuse.
Step 3: Identify the angle of elevation. The angle between the ground and the line of sight to the top of the building is 60 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building).
Step 5: Write the formula. We can express this as: tan(angle) = height / distance. Rearranging gives us: distance = height / tan(angle).
Step 6: Plug in the values. We know the height is 40 meters and the angle is 60 degrees. So we need to find tan(60 degrees).
Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3 (approximately 1.732).
Step 8: Substitute the values into the formula. Distance = 40 / tan(60) = 40 / √3.
Step 9: Calculate the distance. This gives us distance = 40 / 1.732, which is approximately 23.09 meters.
