A person standing on the ground observes the top of a 40 m high building at an a
Practice Questions
Q1
A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
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Questions & Step-by-Step Solutions
A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
Step 1: Understand the problem. We have a building that is 40 meters tall, and we want to find out how far a person is from the building when they see the top of it at a 60-degree angle.
Step 2: Recall the relationship between the height of the building, the distance from the building, and the angle of elevation. We can use the tangent function from trigonometry.
Step 3: Write down the formula for tangent: tan(angle) = opposite side / adjacent side. Here, the opposite side is the height of the building (40 m), and the adjacent side is the distance we want to find.
Step 4: Substitute the known values into the formula: tan(60 degrees) = height (40 m) / distance.
Step 5: We know that tan(60 degrees) is equal to √3. So we can rewrite the equation: √3 = 40 / distance.
Step 6: Rearrange the equation to solve for distance: distance = 40 / √3.
Step 7: Calculate the value of distance. Using a calculator, 40 / √3 is approximately 23.09 m.
Step 8: Round the answer to the nearest whole number if needed. In this case, 23.09 m rounds to 23 m.
Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the observer.
Angle of Elevation – Understanding how to interpret the angle of elevation from the observer's line of sight to the top of the building.
Right Triangle Relationships – The scenario can be visualized as a right triangle where the height of the building is the opposite side and the distance from the building is the adjacent side.
