A man is standing 30 meters away from a tower. If the angle of elevation of the
Practice Questions
Q1
A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
15√3 meters
30 meters
15 meters
10√3 meters
Questions & Step-by-Step Solutions
A man is standing 30 meters away from a tower. If the angle of elevation of the top of the tower from the man's position is 30 degrees, what is the height of the tower?
Step 1: Understand the problem. A man is standing 30 meters away from a tower and looking up at the top of the tower at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the man, the top of the tower, and the base of the tower. The distance from the man to the tower is the base of the triangle.
Step 3: The height of the tower is the opposite side of the triangle, and the distance from the man to the tower is the adjacent side.
Step 4: Use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of the triangle. The formula is: tan(angle) = opposite/adjacent.
Step 5: Rearrange the formula to find the height (opposite side): height = distance * tan(angle).
Step 6: Substitute the values into the formula: height = 30 meters * tan(30 degrees).
Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 8: Now calculate the height: height = 30 * (1/√3).
Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the man and the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for solving problems involving heights and distances.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tower is the opposite side, the distance from the man to the tower is the adjacent side, and the angle of elevation is the angle formed.
