kari is flying a kite. she releases 50 feet of string. what is the approximate difference in the height of…

kari is flying a kite. she releases 50 feet of string. what is the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground? round to the nearest tenth.\n14.2 feet\n17.1 feet\n47.6 feet\n55.2 feet

kari is flying a kite. she releases 50 feet of string. what is the approximate difference in the height of the kite when the string makes a 25° angle with the ground and when the string makes a 45° angle with the ground? round to the nearest tenth.\n14.2 feet\n17.1 feet\n47.6 feet\n55.2 feet

Answer

Explanation:

Step1: Find height when angle is 45°

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the hypotenuse (string length) is 50 feet and $\theta = 45^{\circ}$. So, $h_1 = 50\sin45^{\circ}=50\times\frac{\sqrt{2}}{2}\approx50\times0.707 = 35.35$ feet.

Step2: Find height when angle is 25°

Using $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ again, with $\theta = 25^{\circ}$ and hypotenuse 50 feet. So, $h_2=50\sin25^{\circ}\approx50\times0.423 = 21.15$ feet.

Step3: Calculate the difference

The difference $\Delta h=h_1 - h_2=35.35 - 21.15=14.2$ feet.

Answer:

14.2 feet