Answer:
12
Step-by-step explanation:
hope this helps! :)
Answer: Either 25.0 or 25 depending on how your teacher wants you to format the answer
===========================================================
Explanation:
To start off, it probably helps to translate what the question wants.
It states "For the pilot of airplane B, calculate the angle between the lines of sight to the airplane at C and Jenny's airplane [at point A]".
This fairly long, and possibly complex, sentence boils down to "find angle B"
To find angle B, we need to find the length of side 'a' first
Let,
a = x
b = 4.2
c = 5.7
Note how the lowercase letters (a,b,c) are opposite their uppercase counterparts (A,B,C). This is often the conventional way to label triangles. The lowercase letters are usually for the side lengths while the upper case is for the angles.
We have angle A = 120 degrees
Plug these values into the law of cosines formula below. Then solve for x
a^2 = b^2 + c^2 - 2*b*c*cos(A)
x^2 = 4.2^2 + 5.7^2 - 2*4.2*5.7*cos(120)
x^2 = 17.64 + 32.49 - 47.88*cos(120)
x^2 = 17.64 + 32.49 - 47.88*(-0.5)
x^2 = 17.64 + 32.49 + 23.94
x^2 = 74.07
x = sqrt(74.07)
x = 8.60639297266863
x = 8.6064
So side 'a' is roughly 8.6064 kilometers when we round to four decimal places
Now we'll use this to find angle B
Use the law of cosines again, but this time, the formula is slightly altered so that angle B is the focus instead of angle A
Plug in the side lengths (a,b,c). Solve for angle B
b^2 = a^2 + c^2 - 2*a*c*cos(B)
(4.2)^2 = (8.6064)^2 + (5.7)^2 - 2*(8.6064)*(5.7)*cos(B)
17.64 = 74.07012096 + 32.49 - 98.11296*cos(B)
17.64 = 106.56012096 - 98.11296*cos(B)
17.64 - 106.56012096 = 106.56012096 - 98.11296*cos(B)-106.56012096
-88.92012096 = -98.11296*cos(B)
(-88.92012096)/(-98.11296) = (-98.11296*cos(B))/(-98.11296)
0.906303519535034 = cos(B)
cos(B) = 0.906303519535034
arccos(cos(B)) = arccos(0.906303519535034)
B = 25.0005785532867
It's a bit messier this time around, but we get the approximate angle
B = 25.0005785532867
which rounds to
B = 25.0 degrees
when we round to the nearest tenth. We can write "25.0" as simply "25"
The interest rates required to get a total amount of $2,420 from compound interest on a principal of $2,000 compounded 1 times per year over 2 years is 10% per year.
<h3>What is compound interest?</h3>
The interest on savings that is calculated on both the initial principal and the interest accrued over time is known as compound interest.
The concept of compound interest, also known as "interest on interest," is thought to have first appeared in Italy in the 17th century. It will accelerate the growth of a sum more quickly than simple interest, which is calculated only on the principal sum.
Money is multiplied more quickly through compounding, and the more times it is compounded, the higher the compound interest will be.
Using the formula A = P(1 + r/n)^nt
Solving for rate r as a decimal
r = n[(A/P)^(1/nt) - 1]
r = 1 × [(2,420/2,000)^{1/(1)(2)} - 1]
r = 0.1
Then convert r to R as a percentage
R = r × 100
R = 0.1 × 100
R = 10%/year
Learn more about compound interest
brainly.com/question/12325365
#SPJ9
X = 25 +4*(90 -x) . . . . . x is 25 more than 4 times its complement
x = 385 -4x . . . . . . . . . eliminate parentheses
5x = 385 . . . . . . . . . . . .add 4x
x = 77 . . . . . . . . . . . . . . divide by 5
The measue of angle x is 77°.
