Answer:
The distance between Kirk and Arianna. What's given in the problem Reid is \(4\,\mathrm{meters}\) straight behind Kirk Reid is \(7\,\mathrm{meters}\) directly left of Arianna How to solve Draw a diagram to represent the situation, then use the Pythagorean theorem to find the distance between Kirk and Arianna. Step 1 Draw a diagram. $\begin{tikzpicture}$ $\node at (0,0) {Kirk};$ $\node at (4,0) {Reid};$ $\node at (4,-7) {Arianna};$ $\draw (0,0) -- (4,0) -- (4,-7) -- cycle;$ $\end{tikzpicture}$ Step 2 Use the Pythagorean theorem to find the distance between Kirk and Arianna. \(\sqrt{4^{2}+7^{2}}=\sqrt{65}\approx 8.1\text{\ meters}\) Solution The distance between Kirk and Arianna is approximately \(8.1\,\mathrm{meters}\). Generative AI is experimental, so always double-check the work to ensure accuracy
Answer: 8.1 meters
Step-by-step explanation:
To find the distance between Kirk and Arianna, we can use the Pythagorean theorem since they form a right triangle with Reid being the right angle.
1. Distance Between Kirk and Arianna:
- Kirk is 4 meters straight behind Reid.
- Arianna is 7 meters directly left of Reid.
2. Distance Between Kirk and Arianna (Using Pythagorean Theorem)**:
- The distance between Kirk and Arianna can be calculated as the hypotenuse of a right triangle where the legs are the distances from Kirk to Reid (4 meters) and from Reid to Arianna (7 meters).
- Using the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( c \) is the distance between Kirk and Arianna, \( a \) is the distance from Kirk to Reid (4 meters), and \( b \) is the distance from Reid to Arianna (7 meters).
3. Calculating the Distance:
- \( c = \sqrt{4^2 + 7^2} \)
- \( c = \sqrt{16 + 49} \)
- \( c = \sqrt{65} \)
- \( c \approx 8.1 \) meters (rounded to the nearest tenth)
