Answer:
5.545
Step-by-step explanation:
This problem can be easily solved by using the law of cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
in this case, the formula can be applied in the following way
a^2 = b^2 + c^2 - 2*b*c*cos(α)
Where
a,b,c are each of the sides of the triangle,
α is the angle between sides b and c
(See attached picture)
If we use the formula we get
a^2 = (9)^2 + (6)^2 - 2*(9)(6)*cos(37°)
a^2 = 81 + 36 - 86.2526
a^2 = 30.747
a = sqrt(30.747)
a = 5.545
I got

What we know
cos a=-3/5.
sin b=12/13
Angle A interval are between 180 and 270 or third quadrant
Angle B quadrant is between 90 and 180 or second quadrant.
What we need to find
Cos(b)
Cos(a)
What we are going to apply
Sum and Difference Formulas
Basics Sine and Cosines Identies.
1. Let write out the cos(a-b) formula.

2. Use the interval it gave us.
According to the given, Angle B must between in second quadrant.
Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.
.




so our adjacent side is 5.
Cosine is adjacent/hypotenuse so our cos b=5/13.
Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,
.




so our opposite side is 4. sin =Opposite/Hypotenuse so our sin a =4/5.Sin is negative in the third quadrant so
sin a =-4/5.
Now use cosine difference formula



Hope this helps
Remember your Number system
After the decimal point to the right, the next digit is the TENTH, and next is HUNDREDTH.
So for 26.5 = 26.500.
The tenth digit is 5, and the Hundredth is 0.
After the hundredth digit which is 0, the next digit is also 0.
The second 0 is not up to 5, so we would not add to the first zero.
(Was it 5, or above, we would have added 1 to first zero)
So the answer is 26.50. If the next digit after the hundredth digit was 5 or more the answer would have been 26.51.
But for this question the answer is 26.50 to the nearest hundredth. Cheers.
Answer:
The area of the circle is 
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference of a circle is equal to

we have

assume

substitute the values

![r=31.4/[2(3.14)]=5\ units](https://tex.z-dn.net/?f=r%3D31.4%2F%5B2%283.14%29%5D%3D5%5C%20units)
step 2
Find the area of the circle
The area of the circle is equal to

substitute the values

