Problem One
Remark
This uses the Cosine Law. Two sides and an included angle leaves you with no choice. The good news is that there is never any ambiguity.
Step One
Find the supplement to the 105 degree angle. The supplement will put you inside the triangle which you need to have happen for the cos law.
180 - 105 = 75
Step Two
Set up the Cos Law, You will be solving for b
b^2 = a^2 + c^2 - 2*a*c*Cos(B)
Givens
a =200
B = 75 from step one.
c = 180
Solve
b^2 = 200^2 + 180^2 - 2*180*200*cos(75)
b^2 = 40000 + 32400 - 72000 * cos(75)
b^2 = 72400 - 72000 * 25882
b^2 = 72400 - 18634.97
b^2 =53756.03
b = sqrt(53765.03)
b = 231.9
Problem Two
This is the Sine Law
b / sin(B) = c/Sin(C)
Find C
C = 180 - B - A
C = 180 -37.81 - 113.17
C = 29.02 The sin law will give an ambiguity if you use 12 and 113.17. Better to use an acute angle if you can with the sine law.
Solve
b / sin(B) = c/sin(c)
b / sin(37.81) = 6.33/sin(29.02)
b / 0.6130 = 6.33 / 0.4851
b / 0.6130 = 13.048
b = 13.048 * 0.6130
b = 7.9987 which rounds to 8.
Answer D <<<<
Answer:
70%
Step-by-step explanation:
An easy way to figure this out is like this: Percentage is out of 100 so that would mean 30% is equal to 30/100. Basically, all you need to do is subtract 100-30 and convert to a percent (just add the percent sign). Boom! 70% is your answer!!!!!!! :)
Answer:
You bought 5 books for $60 and 2 movies for $30
Step-by-step explanation:
Answer:
You cannot simplify it any further!!!!
Step-by-step explanation:
Let's simplify step-by-step.
45+32n
Answer:
=32n+45
Answer:
$120
Step-by-step explanation:
Multiply the price of the bike by the discount percentage
150 * 0.20 = 30
Subtract the number you just found from the original price
150 - 30 = 120
There is your answer
You could take a shortcut by doing the following
1 - 0.20 = 0.80
Then multiply the original value by the new percentage
150 * 0.80 = 120
Personally I like the first method because it makes more sense.
