Question

emily has let out 50 meters of kite string. if emily is 35 meters from maggie, how high is the kite above the ground when she notices that her kite is flying directly above her friend?

Explanation:

Step1: Identify the triangle type

This is a right triangle problem, where the kite string is the hypotenuse (\(c = 50\) m), the distance between Emily and Maggie is one leg (\(a = 35\) m), and the height of the kite is the other leg (\(b\)). We use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula

We need to solve for \(b\), so \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(c = 50\) and \(a = 35\): \(b=\sqrt{50^{2}-35^{2}}\).

Step3: Calculate the squares

\(50^{2}=2500\) and \(35^{2}=1225\). Then \(b=\sqrt{2500 - 1225}\).

Step4: Subtract inside the square root

\(2500-1225 = 1275\), so \(b=\sqrt{1275}\approx35.71\) (rounded to two decimal places).

Answer:

The kite is approximately \(\boldsymbol{35.71}\) meters above the ground.