A man is standing on the ground and looking at the top of a 40 m high building.
Practice Questions
Q1
A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
20 m
40 m
20√3 m
40√3 m
Questions & Step-by-Step Solutions
A man is standing on the ground and looking at the top of a 40 m high building. If the angle of elevation is 60 degrees, how far is he from the building?
Step 1: Understand the problem. A man is looking at the top of a 40 m high building from the ground.
Step 2: Identify the angle of elevation. The angle of elevation from the man to the top of the building is 60 degrees.
Step 3: Recall the relationship in a right triangle. 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 for tangent. tan(60°) = height / distance.
Step 5: Substitute the known values into the formula. tan(60°) = 40 m / distance.
Step 7: Calculate tan(60°). The value of tan(60°) is √3.
Step 8: Substitute tan(60°) into the equation. distance = 40 m / √3.
Step 9: Simplify the distance. This can be rewritten as distance = 40/√3 m.
Step 10: Rationalize the denominator. Multiply the numerator and denominator by √3 to get distance = (40√3) / 3 m.
Step 11: Final answer. The distance from the man to the building is approximately 20√3 m.
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 building.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the line of sight.
