Please Answer This question.

K = 15

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine x = 1/4

Cos² x = K / 16

K =?

Next, we shall determine the 3rd leg (i.e the adjacent) of the right angle triangle. This can be obtained as follow:

Sine x = 1/4

Sine x = Opposite / Hypothenus

Opposite = 1

Hypothenus = 4

Adjacent =?

Hypo² = Opp² + Adj²

4² = 1² + Adj²

16 = 1 + Adj²

Collect like terms

16 – 1 = Adj²

15 = Adj²

Take the square root of both side.

Adj = √15

Next, we shall determine Cos² x.

Adjacent = √15

Hypothenus = 4

Cos² x =?

Cos x = Adjacent / Hypothenus

Cos x = √15 /4

Square both side

Cos² x = (√15 /4)²

Cos² x = 15 / 16

Finally, we shall determine the value of K. This can be obtained as follow:

Cos² x = K / 16

Cos² x = 15 / 16

K / 16 = 15 / 16

K = 15