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xxMikexx [17]
3 years ago
6

During a checker game there are 16 pieces left. the ratio of black to red is 3:5. How many black pieces are left on the board?

Mathematics
1 answer:
olganol [36]3 years ago
6 0
We know that there are 16 pieces left and that the ratio is 3 : 5. The ratio teels us there are 8 "parts" inside (because 3 + 5 = 8), so now we may just divide 16 by 8 to find out how much is one such "part":

16 ÷ 8 = 2

Now we can see that one "part" of the ratio is for 2 pieces. So if the ratio of black to red pieces is 3 : 5, then there are 3 * 2 = 6 red pieces and <u>5 * 2 = 10 black bieces</u>.
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Maksim231197 [3]
1) To find x we are going to use the Pythagorean equation:
 x= \sqrt{a^{2}+b^{2}  }
where 
a and b are the legs of our triangle. For our picture we can infer that a=10 and b=8, so lets replace those values in our equation to find x:
x= \sqrt{10^{2}+8^{2}}
x= \sqrt{100+64}
x= \sqrt{164}
x=12.8
We can conclude that the value of x in our triangle is 12.8

2) To find y we are going to use the trigonometric function tangent. Remember that tan(y)= \frac{opposite}{adjacent}. We know that the opposite side of our angle y is 8, and its adjacent side is 10, so lets replace those values in our tangent function to find y:
tan(y)= \frac{8}{10}
tan(y)=0.8
Since we need the measure of angle y, we are going to take inverse tangent to both sides to find it:
y=arctan(0.8)
y=38.66
We can conclude that the value of y in our triangle is 38.66°

3) Finally, to find z we are going to take advantage of two facts: the sum of the interior angles of a triangle is always 180°, and  our triangle is a right one, so one of its sides is 90°. Therefore, y+z+90=180. Since we already know the value of y, lets replace it in our equation and solve for z:
38.66+z+90=180
z+128.66=180
z=51.34
We can conclude that the measure of angle z is 51.34°


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