: Finding ∠A in △ABC
Sum of angles in a triangle:
∠A=180∘−∠B−∠C
∠A=180∘−71∘−67∘=42∘
∠A=42∘
: Finding side b in △ABC
Law of sines:
sin∠Aa=sin∠Bb
b=a⋅sin∠Asin∠B=5 cm⋅sin42∘sin71∘
sin42∘≈0.6694, sin71∘≈0.9455
sin42∘sin71∘≈0.66940.9455≈1.412
b≈5 cm×1.412=7.06 cm
b=7.06 cm
: Finding side c in △ABC
Law of sines:
sin∠Aa=sin∠Cc
c=a⋅sin∠Asin∠C=5 cm⋅sin42∘sin67∘
sin42∘≈0.6694, sin67∘≈0.9205
sin42∘sin67∘≈0.66940.9205≈1.375
c≈5 cm×1.375=6.88 cm
c=6.88 cm
: Finding ∠F in △DEF
Sum of angles in a triangle:
∠F=180∘−∠D−∠E
∠F=180∘−52∘−67∘=61∘
∠F=61∘
: Finding side e in △DEF
Law of sines:
sin∠Dd=sin∠Ee
e=d⋅sin∠Dsin∠E=10 cm⋅sin52∘sin67∘
sin52∘≈0.7880, sin67∘≈0.9205
sin52∘sin67∘≈0.78800.9205≈1.168
e≈10 cm×1.168=11.68 cm
e=11.68 cm
: Finding side f in △DEF
Law of sines:
sin∠Dd=sin∠Ff
f=d⋅sin∠Dsin∠F=10 cm⋅sin52∘sin61∘
sin52∘≈0.7880, sin61∘≈0.8746
sin52∘sin61∘≈0.78800.8746≈1.110
f≈10 cm×1.110=11.10 cm
f=11.10 cm
