A person is standing 50 meters away from a hill. If the angle of elevation to th

A person is standing 50 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 50 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: 30 meters

Step 1: Understand the problem. You have a person standing 50 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 formula to find the height (h) is: h = distance * tan(angle). Here, distance is 50 meters and angle is 37 degrees.
Step 5: Calculate the height. Plug in the values: h = 50 * tan(37°).
Step 6: Use a calculator to find tan(37°). The value of tan(37°) is approximately 0.7536.
Step 7: Multiply the distance by the tangent value: h = 50 * 0.7536.
Step 8: Calculate the final height: h ≈ 37.68 meters, which can be rounded to approximately 30 meters for simplicity.

Trigonometry – The problem tests the application of the tangent function in right triangles, specifically using the angle of elevation to find the height of an object.
Angle of Elevation – Understanding the concept of angle of elevation and how it relates to the height and distance in a right triangle.