SOLUTION: Chris places an orange cone at his current location. Then, he faces west, walks 40 meters, turns 30^{\circ} to his right, and walks 20 meters. How far is Chris from the cone, in me

Algebra ->  Triangles -> SOLUTION: Chris places an orange cone at his current location. Then, he faces west, walks 40 meters, turns 30^{\circ} to his right, and walks 20 meters. How far is Chris from the cone, in me      Log On


   

Question 1210190: Chris places an orange cone at his current location. Then, he faces west, walks 40 meters, turns 30^{\circ} to his right, and walks 20 meters. How far is Chris from the cone, in meters? Round your answer to the nearest whole number.
(You will need to use a calculator.)
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break down this problem step by step.
**1. Visualize the Path**
* Chris starts at a point (the cone).
* He walks 40 meters west.
* He turns 30° to his right (northward direction) and walks 20 meters.
We can represent this as a triangle. Let's label the points:
* **A:** The location of the cone.
* **B:** The point 40 meters west of the cone.
* **C:** Chris's final location.
**2. Apply the Law of Cosines**
We need to find the distance AC. We know:
* AB = 40 meters
* BC = 20 meters
* Angle ABC = 180° - 30° = 150°
The Law of Cosines states:
AC² = AB² + BC² - 2(AB)(BC)cos(∠ABC)
**3. Plug in the Values**
AC² = 40² + 20² - 2(40)(20)cos(150°)
AC² = 1600 + 400 - 1600cos(150°)
**4. Evaluate cos(150°)**
* cos(150°) = -√3 / 2 ≈ -0.866
AC² = 2000 - 1600(-0.866)
AC² = 2000 + 1385.6
AC² = 3385.6
**5. Calculate AC**
AC = √3385.6 ≈ 58.186
**6. Round to the Nearest Whole Number**
AC ≈ 58 meters
**Therefore, Chris is approximately 58 meters from the cone.**