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 !
Answer:
Radius = 5
center is (19,-1)
Step-by-step explanation:
Two points in the plane, (19,4) and (19,−6), represent the endpoints of the diameter of a circle.
Distance between the points is calculated using formula
diameter = 10
radius = diameter divide by 2
Radius = 5
midpoint is the center of the circle
(19,-1)
Equation of the circle
h,k is the center and r is the radius
h=19 and k=-1 , r=5
Answer:
which math question
u didnt provide any
Step-by-step explanation:
Answer:
i did it again i did i did not do did it
Answer:
The answer is 8.
Step-by-step explanation:
The scale factor between the figures is 2/3, this means that the ratio of the smaller figure to the larger figure is 2/3:
.
So when a side of the the larger figure is 12 then:
Therefore
.
Thus the length of the corresponding smaller side is 8.
