Julio says that 6, 7, and 12 will make a right triangle but Matt says they will definitely not. Prove who is correct and show an
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Julio says that 6, 7, and 12 will make a right triangle but Matt says they will definitely not. Prove who is correct and show an example.
The Pythagoras theorem formula states that in a right triangle ABC, the square of the hypotenuse is equal to the sum of the square of the other two legs. If AB, BC, and AC are the sides of the triangle, then: BC2 = AB2 + AC2. While if a, b, and c are the sides of the triangle, then c2 = a2 + b2.
so if c² = a² + b²
12² = 6² + 7²
144 = 36 + 49
144 = 85
it is not a right triangle, so Matt is right
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This is adding two vectors, one magnitude 300 direction east, and one magnitude 100 direction 30 degrees northeast.
For the resulting sum we can use the Law of Cosines or just add up the components. Let's try it both ways.
Components first. In the east direction we have
300 + 100 cos 30° = 300 + 100(√3/2) = 386.60 miles per hour
In the north direction we have
0 + 100 sin 30° = 100 (1/2) = 50 miles per hour
So a total speed of
sqrt{386.6^2 + 50^2} = 389.82 miles per hour
Answer: 389.82
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OK let's try the Law of Cosines. We have sides 300 and 100 and included angle 150°.