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A man flies a kite with a 100 foot string. The angle of elevation of the string is 52^(@). What is the height of the kite in the sky?

A man flies a kite with a 100100 foot string. The angle of elevation of the string is 52∘ 52^{\circ} .\newlineWhat is the height of the kite in the sky?

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Q. A man flies a kite with a 100100 foot string. The angle of elevation of the string is 52∘ 52^{\circ} .\newlineWhat is the height of the kite in the sky?
  1. Trigonometry Calculation: To find the height of the kite, we can use trigonometry, specifically the sine function, since we have the angle of elevation and the length of the string, which acts as the hypotenuse of a right triangle. The sine of an angle in a right triangle is the ratio of the opposite side (the height of the kite, in this case) to the hypotenuse (the length of the string). The formula to use is: height=hypotenuse×sin⁡(angle of elevation)\text{height} = \text{hypotenuse} \times \sin(\text{angle of elevation})
  2. Calculator Setup: First, we need to ensure that our calculator is set to the correct mode (degrees, in this case) because the angle of elevation is given in degrees.
  3. Height Calculation: Now we can calculate the height using the formula:\newlineheight=100 feet×sin⁡(52 degrees)\text{height} = 100 \text{ feet} \times \sin(52 \text{ degrees})\newlineWe use a calculator to find the sine of 5252 degrees.
  4. Sine Calculation: After calculating the sine of 5252 degrees, we find that sin⁡(52∘)≈0.7880\sin(52^\circ) \approx 0.7880 (rounded to four decimal places for precision).
  5. Final Height Calculation: Now we multiply the length of the string by the sine of the angle to find the height: \newlineheight=100 feet×0.7880\text{height} = 100 \text{ feet} \times 0.7880\newlineheight≈78.80 feet\text{height} \approx 78.80 \text{ feet}

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