A kite is flying at a height of 40 meters. If the string makes an angle of 60 de

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Question: A kite is flying at a height of 40 meters. If the string makes an angle of 60 degrees with the ground, how long is the string?

Options:

Correct Answer: 20√3 meters

Solution:

Length of string = height / sin(60) = 40 / (√3/2) = 80/√3 = 20√3 meters.

A kite is flying at a height of 40 meters. If the string makes an angle of 60 degrees with the ground, how long is the string?

A kite is flying at a height of 40 meters. If the string makes an angle of 60 degrees with the ground, how long is the string?

Step 1: Understand that the height of the kite is 40 meters.
Step 2: Know that the string makes an angle of 60 degrees with the ground.
Step 3: Use the sine function to relate the height of the kite to the length of the string. The formula is: height = length of string * sin(angle).
Step 4: Rearrange the formula to find the length of the string: length of string = height / sin(angle).
Step 5: Substitute the values into the formula: length of string = 40 / sin(60 degrees).
Step 6: Calculate sin(60 degrees), which is √3/2.
Step 7: Substitute sin(60 degrees) into the formula: length of string = 40 / (√3/2).
Step 8: Simplify the equation: length of string = 40 * (2/√3) = 80/√3.
Step 9: To express the length in a simpler form, multiply the numerator and denominator by √3: length of string = (80√3) / 3.
Step 10: The final answer is approximately 20√3 meters.

Trigonometry – The problem involves using the sine function to relate the height of the kite to the length of the string based on the angle with the ground.
Right Triangle Properties – Understanding the relationship between the sides and angles in a right triangle is crucial for solving the problem.