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Answer:
cos B = (√5)/5
csc B = (√5)/2
tan A = 1/2
Step-by-step explanation:
The length of hypotenuse AB is given by the Pythagorean theorem:
AB² = AC² +BC²
AB² = 8² +4² = 64 +16 = 80
AB = √80 = 4√5
The mnemonic SOH CAH TOA can help you remember the needed ratios.
Cos = Adjacent/Hypotenuse
cos B = BC/AB = 4/(4√5)
cos B = (√5)/5
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Sin = Opposite/Hypotenuse
csc = 1/sin = Hypotenuse/Opposite
csc B = AB/AC = (4√5)/8
csc B = (√5)/2
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Tan = Opposite/Adjacent
tan A = BC/AC = 4/8
tan A = 1/2