Answer:
K = 15
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