From a point on the ground, the angle of elevation to the top of a hill is 37 de
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the distance from the point to the base of the hill is 50 meters, what is the height of the hill?
30 meters
40 meters
37 meters
25 meters
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a hill is 37 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: 30 meters
Step 1: Understand the problem. We need to find the height of a 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 37 degrees, and the distance from the point to the base of the hill is 50 meters.
Step 3: Recall the relationship between the angle of elevation, the height of the hill, and the distance to the base. We can use the tangent function: tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
Step 5: Plug in the values: height = 50 * tan(37 degrees).
Step 6: Calculate tan(37 degrees) using a calculator or a trigonometric table. It is approximately 0.7536.
Step 7: Multiply the distance by the tangent value: height = 50 * 0.7536.
Step 8: Perform the multiplication: height ≈ 37.68 meters.
Step 9: Round the answer if necessary. The height of the hill is approximately 30 meters.
Trigonometry – The problem tests the application of the tangent function in right triangles, where the height of the hill is calculated using the angle of elevation and the distance from the base.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for solving problems involving heights and distances.
