From a point on the ground, the angle of elevation to the top of a 12-meter tall

From a point on the ground, the angle of elevation to the top of a 12-meter tall pole is 60 degrees. How far is the point from the base of the pole?

From a point on the ground, the angle of elevation to the top of a 12-meter tall pole is 60 degrees. How far is the point from the base of the pole?

Correct Answer: 6 meters

Step 1: Understand the problem. We have a pole that is 12 meters tall and we want to find out how far away we are from the base of the pole.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is 60 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).
Step 4: Write the formula. We can write this as: tan(60 degrees) = height / distance.
Step 5: Plug in the values. We know the height is 12 meters, so we have: tan(60) = 12 / distance.
Step 6: Rearrange the formula to find distance. This gives us: distance = height / tan(60).
Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 8: Substitute tan(60) into the formula. Now we have: distance = 12 / √3.
Step 9: Calculate the distance. This simplifies to approximately 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 base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the pole, the ground, and the line of sight.