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 20 meters, what is the height of the hill?
10√3 meters
20 meters
30 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 20 meters, what is the height of the hill?
Step 1: Understand the problem. We need to find the height of the hill using the angle of elevation and the distance from the point to the base of the hill.
Step 2: Identify the given information. The angle of elevation is 30 degrees, and the distance from the point to the base of the hill is 20 meters.
Step 3: Recall the relationship between the angle of elevation, height, and distance. We can use the tangent function: tan(angle) = height / distance.
Step 4: Write the formula using the given angle. For 30 degrees, we have: tan(30 degrees) = height / 20 meters.
Step 5: Find the value of tan(30 degrees). It is equal to 1/√3.
Step 6: Substitute the value of tan(30 degrees) into the formula: 1/√3 = height / 20.
Step 7: Rearrange the formula to solve for height: height = 20 * (1/√3).
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.
