If the angle of elevation to the top of a tower from a point 40 meters away is 3

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Question: If the angle of elevation to the top of a tower from a point 40 meters away is 30 degrees, what is the height of the tower?

Options:

Correct Answer: 20√3 meters

Solution:

Using tan(30°) = height/40, height = 40 * (1/√3) = 40/√3 = 20√3 meters.

If the angle of elevation to the top of a tower from a point 40 meters away is 30 degrees, what is the height of the tower?

If the angle of elevation to the top of a tower from a point 40 meters away is 30 degrees, what is the height of the tower?

Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your eye level to the top of the tower.
Step 2: Identify the distance from the point to the base of the tower, which is 40 meters.
Step 3: Recognize that we can use the tangent function (tan) to find the height of the tower. The formula is: tan(angle) = opposite/adjacent.
Step 4: In this case, the 'opposite' side is the height of the tower, and the 'adjacent' side is the distance from the point to the tower (40 meters).
Step 5: Substitute the known values into the formula: tan(30°) = height/40.
Step 6: Calculate tan(30°), which is equal to 1/√3.
Step 7: Set up the equation: 1/√3 = height/40.
Step 8: To find the height, multiply both sides by 40: height = 40 * (1/√3).
Step 9: Simplify the expression: height = 40/√3.
Step 10: To make it easier to understand, multiply the numerator and denominator by √3: height = (40√3)/3.
Step 11: The final height of the tower is approximately 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.