From a point on the ground, the angle of elevation to the top of a hill is 37 de
Practice Questions
Q1
From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the point is 50 meters away from the base of the hill, what is the height of the hill?
30 meters
37 meters
40 meters
50 meters
Questions & Step-by-Step Solutions
From a point on the ground, the angle of elevation to the top of a hill is 37 degrees. If the point is 50 meters away from the base of the hill, what is the height of the hill?
Correct Answer: 37.65 meters
Step 1: Understand the problem. We need to find the height of a hill using the angle of elevation and the distance from the point to the base of the hill.
Step 2: Identify the given information. The angle of elevation is 37 degrees, and the distance from the point to the base of the hill is 50 meters.
Step 3: Recall the relationship between the angle of elevation, the height of the hill, and the distance from the point to the base of the hill. We can use the tangent function: tan(angle) = opposite/adjacent.
Step 4: In our case, the 'opposite' side is the height of the hill (which we want to find), and the 'adjacent' side is the distance from the point to the base of the hill (50 meters).
Step 5: Set up the equation using the tangent function: tan(37 degrees) = height / 50 meters.
Step 6: Rearrange the equation to solve for height: height = 50 meters * tan(37 degrees).
Step 7: Calculate tan(37 degrees) using a calculator or a trigonometric table. It is approximately 0.753.
Step 8: Multiply 50 meters by 0.753 to find the height: height = 50 * 0.753.
Step 9: Perform the multiplication: height ≈ 37.65 meters.
Trigonometry – The problem tests the application of trigonometric functions, specifically the tangent function, to find the height of an object based on an angle of elevation and a horizontal distance.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance from the point to the base, and the angle of elevation.
