A person looks at the top of a building from a distance of 50 meters. If the ang

A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

Correct Answer: 25 meters

Step 1: Understand the problem. You are looking at the top of a building from a distance of 50 meters away.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the building is 30 degrees.
Step 3: Recall the relationship in a right triangle. The height of the building (opposite side) and the distance from the building (adjacent side) can be related using the tangent function.
Step 4: Write the formula for tangent. The formula is: tan(angle) = opposite/adjacent.
Step 5: Substitute the known values into the formula. Here, opposite is the height of the building (H), and adjacent is the distance (50 meters). So, tan(30 degrees) = H / 50.
Step 6: Solve for the height (H). Rearranging gives H = 50 * tan(30 degrees).
Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 8: Substitute this value back into the equation. H = 50 * (1/√3).
Step 9: Calculate the height. H ≈ 50 * 0.577 ≈ 25 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 it.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is the opposite side, the distance is the adjacent side, and the angle of elevation is given.