What is the right triangle definition of the cosecant function?

a. hypotenuse/adjacent
b. opposite/hypotenuse
c. adjacent/hypotenuse
d. hypotenuse/opposite
e. opposite/adjacent

  D. hypotenuse/opposite

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

You know that

  csc = 1/sin

so

  csc = 1/(opposite/hypotenuse) = hypotenuse/opposite . . . . matches D

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !