A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Practice Questions
1 question
Q1
A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Q: A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Step 1: Understand the situation. A person is standing 40 meters away from a building and looking up at the top of the building.
Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the building is 30 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building).
Step 4: Write the formula. Height = distance * tan(angle). Here, distance = 40 meters and angle = 30 degrees.
Step 5: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Substitute the values into the formula. Height = 40 * (1/√3).
Step 7: Calculate the height. Height = 40/√3.
Step 8: Simplify the height. Height = 10√3 meters.
