Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the lib
rary. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle. A triangle has points labeled Library, Mall, and Home The largest angle formed during his trip is _______. At his home at the mall between the mall and the library between his home and the library
2 answers:
Answer: The largest angle formed during his trip is at the mall between his home and the library.
Step-by-step explanation:
Hi, since the situation forms a right triangle (see image attached) the angle formed between his home and the library is 90°.
The sum of the interior angles of a right triangle is 180°, and the right angle (90°)is the largest angle formed.
So, the largest angle formed during his trip is at the mall between his home and the library.
Feel free to ask for more if needed or if you did not understand something.
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Answer:
distance: 320.624 miles
direction: 43.576°
Step-by-step explanation:
The speed and direction can be found by adding the given vectors.
... 320∠40° + 20∠130°
... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))
... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)
The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.
... = √(232.278² +221.013²)∠arctan(221.013/232.278)
... = 320.624∠43.576°
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A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.
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<em>Comment on coordinate systems</em>
Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.
Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.
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Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.
