From a point on the ground, the angle of elevation to the top of a 20-meter tall
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a 20-meter tall building is 45 degrees. How far is the point from the base of the building?
10 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 20-meter tall building is 45 degrees. How far is the point from the base of the building?
Correct Answer: 20 meters
Step 1: Understand the problem. We have a building that is 20 meters tall.
Step 2: Identify the angle of elevation from the point on the ground to the top of the building, which is 45 degrees.
Step 3: Recall the relationship between the height of the building, the distance from the point to the base of the building, and the angle of elevation. We can use the tangent function.
Step 4: The formula for tangent is: tan(angle) = opposite / adjacent. Here, the opposite side is the height of the building (20 meters) and the adjacent side is the distance we want to find.
Step 5: For an angle of 45 degrees, the value of tan(45 degrees) is 1.
Step 6: Set up the equation: tan(45 degrees) = height / distance. This means 1 = 20 / distance.
Step 7: Rearrange the equation to find the distance: distance = height / tan(45 degrees).
Step 8: Substitute the values: distance = 20 / 1.
Step 9: Calculate the distance: distance = 20 meters.
Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building 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 building, the distance from the point to the base, and the angle of elevation.
