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 point is 100 meters away from the base of the hill, what is the height of the hill?
50 meters
100 meters
100√3 meters
50√3 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 point is 100 meters away from the base of the hill, what is the height of the hill?
Correct Answer: 50√3 meters
Step 1: Understand the problem. We have a point on the ground and a hill. We need to find the height of the hill.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the hill is given as 30 degrees.
Step 3: Identify the distance from the point to the base of the hill. This distance is 100 meters.
Step 4: Use the tangent function. The height of the hill can be found using the formula: Height = distance * tan(angle).
Step 5: Calculate the tangent of the angle. For 30 degrees, tan(30 degrees) = 1/√3.
Step 6: Substitute the values into the formula. Height = 100 * (1/√3).
Step 7: Simplify the calculation. This gives us Height = 100/√3.
Step 8: To express the height in a simpler form, multiply the numerator and denominator by √3. This gives us Height = 100√3/3.
Step 9: Calculate the final height. The height of the hill is approximately 50√3 meters.
Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to calculate height using the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation and its application in real-world scenarios.
Right Triangle Properties – Utilizing properties of right triangles to relate angles and side lengths.
