Question: A man is 50 meters away from a tower. If he looks up at an angle of 45 degrees to see the top of the tower, what is the height of the tower?
Options:
25 meters
50 meters
75 meters
100 meters
Correct Answer: 50 meters
Solution:
Height = distance * tan(45) = 50 * 1 = 50 meters.
A man is 50 meters away from a tower. If he looks up at an angle of 45 degrees t
Practice Questions
Q1
A man is 50 meters away from a tower. If he looks up at an angle of 45 degrees to see the top of the tower, what is the height of the tower?
25 meters
50 meters
75 meters
100 meters
Questions & Step-by-Step Solutions
A man is 50 meters away from a tower. If he looks up at an angle of 45 degrees to see the top of the tower, what is the height of the tower?
Step 1: Understand the situation. A man is standing 50 meters away from a tower.
Step 2: The man looks up at an angle of 45 degrees to see the top of the tower.
Step 3: Recognize that the angle of 45 degrees means that the height of the tower and the distance from the man to the tower form a right triangle.
Step 4: In a right triangle, the tangent of an angle is equal to the opposite side (height of the tower) divided by the adjacent side (distance from the man to the tower).
Step 5: Use the formula: tan(angle) = opposite/adjacent. Here, angle = 45 degrees, opposite = height of the tower, and adjacent = 50 meters.
Step 6: Since tan(45 degrees) = 1, we can write the equation as: height = distance * tan(45).
Step 7: Substitute the values into the equation: height = 50 meters * 1.
Step 8: Calculate the height: height = 50 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the man to the tower and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line of sight to the line of sight to the top of the tower.
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 45 degrees.
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