If the angle of elevation from a point 30 meters away from the base of a hill is

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Question: If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?

Options:

Correct Answer: 15√3 meters

Solution:

Using the tangent function, tan(60) = height / 30. Therefore, height = 30 * tan(60) = 30 * √3 = 30√3 meters.

If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?

If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?

Step 1: Understand the problem. We have a point that is 30 meters away from the base of a hill, and we want to find the height of the hill.
Step 2: Draw a right triangle. The distance from the point to the base of the hill is one side (30 meters), the height of the hill is the other side, and the angle of elevation (60 degrees) is between the ground and the line of sight to the top of the hill.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the hill) to the adjacent side (distance from the point to the base of the hill).
Step 4: Write the equation using the tangent function: tan(60 degrees) = height / 30 meters.
Step 5: Rearrange the equation to solve for height: height = 30 * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Substitute the value of tan(60 degrees) into the equation: height = 30 * √3.
Step 8: Simplify the expression: height = 30√3 meters.

Trigonometric Functions – Understanding and applying the tangent function to relate angles and side lengths in right triangles.
Angle of Elevation – Recognizing how the angle of elevation relates to the height of an object and the distance from the observer.
Right Triangle Properties – Using properties of right triangles to solve for unknown lengths based on given angles and distances.