A person standing 100 meters away from a hill observes the top of the hill at an

A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

Correct Answer: 173.21 meters

Step 1: Understand the problem. You have a person standing 100 meters away from a hill and looking up at the top of the hill.
Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the hill is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the hill) divided by the adjacent side (distance from the hill).
Step 4: Set up the equation. The formula is: height = distance * tan(angle). Here, distance is 100 meters and angle is 60 degrees.
Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 6: Substitute the values into the equation. height = 100 * tan(60) = 100 * √3.
Step 7: Simplify the calculation. The height of the hill is 100√3 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the observer.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the hill is the opposite side, the distance from the observer is the adjacent side, and the angle of elevation is given.