Answer:
(1.5,1)
Step-by-step explanation:
The midpoint of G and H is at (2,2).
The midpoint if J and K is (1,0)
The midpoint of the two midpoints is (1.5,1)
You could also i.e. directly ask for the midpoint of H an K, OR, G and J, and you would get the same final result.
As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
The scale is 1:4, as the poster's dimensions are 4 times larger than the scale drawing, which is represented by the second number in the ratio. To see this, you need to see that 15 goes into 60 four times and 20 goes into 80 four times. I hope this helped you!
Answer:
1/7
Step-by-step explanation:
just multiply 1/4 with 1/3
1/4 × 1/3 = 1/7
