Question

a kite is flying 10 ft on the ground. its line is pulled taut and casts a 7 - ft shadow. find the length of the line. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

This is a right triangle with legs 7 ft and 10 ft, and hypotenuse \( x \) (the kite line). Use the Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( a = 7 \), \( b = 10 \), \( c = x \).

Step2: Apply the Pythagorean theorem

Substitute values: \( 7^2 + 10^2 = x^2 \)
Calculate: \( 49 + 100 = x^2 \)
\( 149 = x^2 \)

Step3: Solve for \( x \)

Take square root: \( x = \sqrt{149} \approx 12.2 \)

Answer:

12.2