From a point 60 meters away from the base of a hill, the angle of elevation to t

From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

Correct Answer: 34.64 meters

Step 1: Understand the problem. You are looking for the height of a hill from a point 60 meters away.
Step 2: Identify the angle of elevation. The angle given is 30 degrees.
Step 3: Recall the relationship between the height of the hill, the distance from the hill, and the angle of elevation. This can be calculated using the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Substitute the values into the formula. Here, distance = 60 meters and angle = 30 degrees.
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
Step 7: Multiply the distance by the tangent value: height = 60 * (1/√3).
Step 8: Calculate the height: height = 60 / 1.732, which is approximately 34.64 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance from the base, and the angle of elevation.