A kite is flying at a height of 45 meters. If the string makes an angle of 30° w

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Question: A kite is flying at a height of 45 meters. If the string makes an angle of 30° with the horizontal, how long is the string?

Options:

Correct Answer: 45√3 meters

Solution:

Using sin(30°) = height/string length, string length = height/sin(30°) = 45/(1/2) = 90 meters.

A kite is flying at a height of 45 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 45 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 45 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: For our problem, the opposite side is the height (45 meters) and the angle is 30°. So we write: sin(30°) = height / string length.
Step 5: We know that sin(30°) equals 1/2.
Step 6: Substitute the values into the equation: 1/2 = 45 / string length.
Step 7: Rearrange the equation to find the string length: string length = height / (1/2).
Step 8: Calculate the string length: string length = 45 / (1/2) = 45 * 2 = 90 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 horizontal.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height, the string, and the horizontal distance.