Step 1: Understand the problem. You have a person standing 50 meters away from a hill and looking up at the top of the hill at an angle of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the hill, the other side is the distance from the person to the base of the hill (50 meters), and the angle between the ground and the line of sight to the top of the hill is 30 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 person to the hill). So, tan(30 degrees) = height / 50 meters.
Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 5: Set up the equation. Now, you can write the equation: height = 50 * tan(30 degrees).
Step 6: Substitute the value of tan(30 degrees) into the equation. This gives you height = 50 * (1/√3).
Step 7: Simplify the equation. This means height = 50/√3.
Step 8: To make it easier to understand, you can multiply the numerator and denominator by √3. This gives you height = (50√3)/3.
Step 9: Calculate the height. The final height of the hill is approximately 25√3 meters.
