Answer:
See below
Step-by-step explanation:
Finding a:
[tex]\displaystyle sin (\theta) = \frac{opposite }{hypotenuse}[/tex]
Where θ = 45° , opposite = a, hyp = 4√2
[tex]\displaystyle sin (45)=\frac{a}{4\sqrt{2} } \\\\\frac{1}{\sqrt{2} } = \frac{a}{4\sqrt{2} } \\\\1 = \frac{a}{4} \\\\\boxed{a = 4}[/tex]
Finding c:
[tex]\displaystyle tan (\theta) = \frac{opposite }{adjacent}[/tex]
Where θ = 45°, opposite = 4, adjacent = c
tan 45 = 4 / c
1 = 4 / c
Multiply both sides by c
c = 4
Finding b:
[tex]\displaystyle sin(\theta) = \frac{opposite}{hypotenuse}[/tex]
Where θ = 30°, opposite = a(4), hypotenuse = b
sin 30 = 4 / b
[tex]\displaystyle \frac{1}{2} = \frac{4}{b}[/tex]
Cross Multiply
1 * b = 4 * 2
b = 8
Finding d:
[tex]\displaystyle tan (\theta) = \frac{opposite }{adjacent}[/tex]
Where θ = 30°, opposite = a(4) , adjacent = d
tan 30 = 4 / d
[tex]\displaystyle \frac{1}{\sqrt{3} } = \frac{4}{d} \\\\[/tex]
Cross Multiplying
1 * d = 4√3
[tex]\boxed{d = 4\sqrt{3}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807
