Answer: a = 5; b = 5; c = 10; d = 5[tex]\sqrt{3}[/tex]; e = 5[tex]\sqrt{2}[/tex]; f = 6.93; g = 13
[tex]A_{H}[/tex] = 12.5; [tex]A_{J}[/tex] = 55; [tex]A_{K}[/tex] = 12.5[tex]\sqrt{3}[/tex]; [tex]A_{L}[/tex] = 38.1
Step-by-step explanation:
Value of e:
sin 45 = [tex]\frac{5}{e}[/tex]
e = 5.[tex]\frac{2}{\sqrt{2} }[/tex]
e = 5[tex]\sqrt{2}[/tex]
Value of a:
e² = 5² + a²
a = [tex]\sqrt{ (5\sqrt{2} )^{2} - 5^{2} }[/tex]
a = 5
Value of b:
The figure J is a rectangle, so opposite sides have the same value. Since b is opposite side of the side measuring 5, b = 5.
Value of c:
sin 30 = [tex]\frac{5}{c}[/tex]
c = 5. 2
c = 10
Value of d:
cos 30 = [tex]\frac{d}{10}[/tex]
d = 10.[tex]\frac{\sqrt{3} }{2}[/tex]
d = 5[tex]\sqrt{3}[/tex]
Value of g:
cos 56 = [tex]\frac{11}{g}[/tex]
g = [tex]\frac{11}{0.8532}[/tex]
g = 13
Value of f:
g² = 11² + f²
f = [tex]\sqrt{169 - 121}[/tex]
f = 7
Area of H:
[tex]A_{H}[/tex] = [tex]\frac{5.5}{2}[/tex]
[tex]A_{H}[/tex] = 12.5
Area of J:
[tex]A_{J}[/tex] = 11.5
[tex]A_{J}[/tex] = 55
Area of K:
[tex]A_{K}[/tex] = [tex]\frac{5\sqrt{3}.5 }{2}[/tex]
[tex]A_{K}[/tex] = 12.5[tex]\sqrt{3}[/tex]
Area of L:
[tex]A_{L}[/tex] = [tex]\frac{11.7}{2}[/tex]
[tex]A_{L}[/tex] = 38.5