Answer:
See below
Step-by-step explanation:
<u>Finding a:</u>
![\displaystyle sin (\theta) = \frac{opposite }{hypotenuse}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20sin%20%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopposite%20%7D%7Bhypotenuse%7D)
Where θ = 45° , opposite = a, hyp = 4√2
![\displaystyle sin (45)=\frac{a}{4\sqrt{2} } \\\\\frac{1}{\sqrt{2} } = \frac{a}{4\sqrt{2} } \\\\1 = \frac{a}{4} \\\\\boxed{a = 4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20sin%20%2845%29%3D%5Cfrac%7Ba%7D%7B4%5Csqrt%7B2%7D%20%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20%3D%20%5Cfrac%7Ba%7D%7B4%5Csqrt%7B2%7D%20%7D%20%5C%5C%5C%5C1%20%3D%20%5Cfrac%7Ba%7D%7B4%7D%20%5C%5C%5C%5C%5Cboxed%7Ba%20%3D%204%7D)
<u>Finding c:</u>
![\displaystyle tan (\theta) = \frac{opposite }{adjacent}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%20%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopposite%20%7D%7Badjacent%7D)
Where θ = 45°, opposite = 4, adjacent = c
tan 45 = 4 / c
1 = 4 / c
Multiply both sides by c
c = 4
<u>Finding b:</u>
![\displaystyle sin(\theta) = \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20sin%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
Where θ = 30°, opposite = a(4), hypotenuse = b
sin 30 = 4 / b
![\displaystyle \frac{1}{2} = \frac{4}{b}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7Bb%7D)
Cross Multiply
1 * b = 4 * 2
b = 8
<u>Finding d:</u>
![\displaystyle tan (\theta) = \frac{opposite }{adjacent}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%20%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopposite%20%7D%7Badjacent%7D)
Where θ = 30°, opposite = a(4) , adjacent = d
tan 30 = 4 / d
![\displaystyle \frac{1}{\sqrt{3} } = \frac{4}{d} \\\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%20%7D%20%3D%20%5Cfrac%7B4%7D%7Bd%7D%20%5C%5C%5C%5C)
Cross Multiplying
1 * d = 4√3
![\boxed{d = 4\sqrt{3}}](https://tex.z-dn.net/?f=%5Cboxed%7Bd%20%3D%204%5Csqrt%7B3%7D%7D)
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Answer: 18.09yd
Step-by-step explanation:
A=πr^2
A= 3.14*2.4^2
A= 18.09yd
9, 15, and 21 they are all odd numbers but are not all only divisible by 1; therefore, they are not prime numbers
call x is the amount of cup of pineapple, and y is the amount of cup of cranberry.
we have:
x + y = 10
x/y = 3/2 => x = (3/2)*y
x + y = 10
=> (3/2)y + y = 10
=> 3y + 2y = 20
=> 5y = 20
=> y = 4
x + y =10
=> x = 10 -4 = 6
=> 6 cups of pineapple and 4 cups of cranberry would make 10 cups
Answer:Takeyour time
Step-by-step explanation: