From a point 40 meters away from the base of a tower, the angle of elevation to

From a point 40 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 degrees. What is the height of the tower?

From a point 40 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 degrees. What is the height of the tower?

Correct Answer: 20√3 meters

Step 1: Understand the problem. You have a tower and you are standing 40 meters away from its base.
Step 2: Identify the angle of elevation. The angle from your line of sight to the top of the tower is 30 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the tower) divided by the adjacent side (distance from the tower).
Step 4: Write the formula. Height = distance * tan(angle). Here, distance = 40 meters and angle = 30 degrees.
Step 5: Find tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Substitute the values into the formula. Height = 40 * (1/√3).
Step 7: Simplify the calculation. Height = 40/√3.
Step 8: Further simplify if needed. Height = 40/√3 can be expressed as 20√3 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the tower.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tower, the distance from the tower, and the angle of elevation.