A person is standing 25 meters away from a hill. If the angle of elevation to th

A person is standing 25 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

A person is standing 25 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

Correct Answer: 20 meters

Step 1: Understand the problem. You have a person standing 25 meters away from a hill and you need to find the height of the hill.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the hill is given as 37 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 height of the hill can be calculated using the formula: Height = distance * tan(angle).
Step 5: Plug in the values. Here, distance = 25 meters and angle = 37 degrees. So, Height = 25 * tan(37).
Step 6: Calculate tan(37 degrees). The value of tan(37 degrees) is approximately 0.7536.
Step 7: Multiply the distance by the tangent value. Height = 25 * 0.7536.
Step 8: Perform the multiplication. Height ≈ 18.84 meters.
Step 9: Round the answer. The height of the hill is approximately 20 meters when rounded.

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 hill.
Angle of Elevation – Understanding how the angle of elevation is used to calculate the height of an object based on a horizontal distance.
Rounding – The importance of rounding the final answer correctly based on significant figures or context.