If a kite is flying at a height of 40 meters and the string makes an angle of 30

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Question: If a kite is flying at a height of 40 meters and the string makes an angle of 30 degrees with the ground, how long is the string?

Options:

Correct Answer: 40√3 meters

Solution:

Length of string = height / sin(30) = 40 / 0.5 = 80 meters.

If a kite is flying at a height of 40 meters and the string makes an angle of 30 degrees with the ground, how long is the string?

If a kite is flying at a height of 40 meters and the string makes an angle of 30 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 30 degrees with the ground.
Step 3: Recognize that we can use the sine function to find the length of the string.
Step 4: Recall the sine formula: sin(angle) = opposite side / hypotenuse.
Step 5: In this case, the opposite side is the height of the kite (40 meters) and the hypotenuse is the length of the string.
Step 6: Set up the equation: sin(30 degrees) = height / length of string.
Step 7: Substitute the known values: sin(30 degrees) = 40 / length of string.
Step 8: Calculate sin(30 degrees), which is 0.5.
Step 9: Rewrite the equation: 0.5 = 40 / length of string.
Step 10: Rearrange the equation to find the length of the string: length of string = 40 / 0.5.
Step 11: Calculate the length of the string: 40 / 0.5 = 80 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 of a right triangle is essential for solving the problem.