Question

Create three problems that require you to solve each using each of the trig ratios (one problem where you will use sine, one problem where you will use tangent and one problem where you will use cosine) and then solve each problem, show all your work.

Answer 1

See the attached image for the drawings of the problems. The figures are not to scale. The decimal values in each figure are approximate to one decimal place.

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Focus on Figure 1

sin(angle) = opposite/hypotenuse
sin(A) = BC/AC
sin(36) = 13.2/x
x*sin(36) = 13.2
x = 13.2/sin(36)
x = 13.2/0.58778525229248 <<-- make sure calc is in degree mode
x = 22.4571813404936
x = 22.5
This value is approximate (rounded to one decimal place)

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Move onto Figure 2

cos(angle) = adjacent/hypotenuse
cos(D) = DE/FD
cos(50) = y/57.4
57.4*cos(50) = y
y = 57.4*cos(50)
y = 57.4*0.64278760968653
y = 36.8960087960069
y = 36.9
This value is approximate (rounded to one decimal place)

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Finally, move onto Figure 3

tan(angle) = opposite/adjacent
tan(G) = JH/GH
tan(18) = z/10
10*tan(18) = z
z = 10*tan(18)
z = 10*0.3249196962329
z = 3.249196962329
z = 3.2
This value is approximate (rounded to one decimal place)