If the angle of elevation from a point 50 meters away from a tower is 60 degrees

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Question: If the angle of elevation from a point 50 meters away from a tower is 60 degrees, what is the height of the tower?

Options:

Correct Answer: 25√3 meters

Solution:

Using the tangent function, tan(60) = height / 50. Therefore, height = 50 * tan(60) = 50 * √3 ≈ 86.6 meters.

If the angle of elevation from a point 50 meters away from a tower is 60 degrees, what is the height of the tower?

If the angle of elevation from a point 50 meters away from a tower is 60 degrees, what is the height of the tower?

Step 1: Understand the problem. We have a tower and a point 50 meters away from the base of the tower.
Step 2: Identify the angle of elevation. The angle of elevation from the point to the top of the tower is 60 degrees.
Step 3: Recall the tangent function. In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the tower).
Step 4: Set up the equation using the tangent function. We have tan(60 degrees) = height / 50 meters.
Step 5: Rearrange the equation to find the height. Multiply both sides by 50: height = 50 * 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 = 50 * √3.
Step 8: Calculate the height. Using the approximate value of √3 (about 1.732), we find height ≈ 50 * 1.732 ≈ 86.6 meters.

Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal point to the top of a vertical structure.