A kite is flying at a height of 40 meters. If the string makes an angle of 30° w

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Question: A kite is flying at a height of 40 meters. If the string makes an angle of 30° with the horizontal, how long is the string?

Options:

Correct Answer: 60 meters

Solution:

Using sin(30°) = height/string length, string length = 40/sin(30°) = 40/0.5 = 80 meters.

A kite is flying at a height of 40 meters. If the string makes an angle of 30° with the horizontal, how long is the string?

A kite is flying at a height of 40 meters. If the string makes an angle of 30° with the horizontal, 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° with the horizontal.
Step 3: Use the sine function, which relates the height of the kite to the length of the string. The formula is: sin(angle) = opposite side (height) / hypotenuse (string length).
Step 4: Substitute the known values into the formula: sin(30°) = height / string length.
Step 5: Since the height is 40 meters, rewrite the equation: sin(30°) = 40 / string length.
Step 6: We know that sin(30°) = 0.5.
Step 7: Replace sin(30°) in the equation: 0.5 = 40 / string length.
Step 8: To find the string length, rearrange the equation: string length = 40 / 0.5.
Step 9: Calculate the string length: 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 and the angle it makes with the horizontal.
Right Triangle Properties – Understanding the relationship between the sides and angles of a right triangle is essential for solving the problem.