From a point on the ground, the angle of elevation to the top of a hill is 30 de
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
25 meters
30 meters
35 meters
40 meters
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
Correct Answer: 28.87 meters
Step 1: Understand the problem. We need to find the height of a hill given the angle of elevation and the distance from the point to the base of the hill.
Step 2: Identify the angle of elevation. The angle given is 30 degrees.
Step 3: Identify the distance from the point to the base of the hill. This distance is 50 meters.
Step 4: Use the tangent function. The formula to find the height (h) using the tangent of the angle is: h = distance * tan(angle).
Step 5: Substitute the values into the formula. Here, h = 50 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 (approximately 0.577).
Step 7: Multiply the distance by the tangent value. So, h = 50 * (1/√3).
Step 8: Calculate the height. This gives us h ≈ 50 * 0.577 ≈ 28.87 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 point to the base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance to the base, and the angle of elevation.
