Right Triangle ABC has its right angle at C, BC = 4, and AC= 8. What is the value of the trigonometric ratio?

cos B
csc B
tan A

Drag a value to each box to match the trigonometric ratio?

9514 1404 393

 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

__

  Sin = Opposite/Hypotenuse

  csc = 1/sin = Hypotenuse/Opposite

  csc B = AB/AC = (4√5)/8

  csc B = (√5)/2

__

  Tan = Opposite/Adjacent

  tan A = BC/AC = 4/8

  tan A = 1/2