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Answer:
The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.
Step-by-step explanation:
The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.
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Whatever% of anything is just (whatever/100) * anything.
let's say we'll add "x" cups of pure vinegar, pure vinegar meaning is 100% vinegar.
how much vinegar is there in "x" cups of 100% vinegar? well (100/100) * x, or just "x".
how much vinegar is there in 10 cups of 10% vinegar? well, (10/100) * 10, or just 1.
say after adding the "x" cups to the 10 cups, we end up with "y" cups, of 50% of vinegar.
how much is 50% of y? well, (50/100) * y or 0.5y.
bearing in mind that x+10 = y, both cups amounts added up, and that x+1=0.5y, both vinegar amounts added up, thus
let's say we'll add "x" cups of pure vinegar, pure vinegar meaning is 100% vinegar.
how much vinegar is there in "x" cups of 100% vinegar? well (100/100) * x, or just "x".
how much vinegar is there in 10 cups of 10% vinegar? well, (10/100) * 10, or just 1.
say after adding the "x" cups to the 10 cups, we end up with "y" cups, of 50% of vinegar.
how much is 50% of y? well, (50/100) * y or 0.5y.
bearing in mind that x+10 = y, both cups amounts added up, and that x+1=0.5y, both vinegar amounts added up, thus