Which of the following is correct based on this picture? A. tan M=38/63 B. sin M=38/63 C. none of these are correct D. cos M=38/63

Option D. Cos M = 38/63

Step-by-step explanation:

Let the side opposite to angle M be y.

The value of y can be obtained by using the pythagoras theory as illustrated below:

y² = 63² – 38²

y² = 3969 – 1444

y² = 2525

Take the square root of both side

y = √2525

y = √(25 x 101)

y = √25 x √101

y = 5√101

Now, let us determine Tan M, Sine M and Cos M to know which of the options are correct.

This is illustrated below:

Tan M =?

Opposite = 5√101

Adjacent = 38

Tan M = Opposite /Adjacent

Tan M = 5√101 / 38

Sine M =.?

Opposite = 5√101

Hypothenus = 63

Sine M = Opposite /Hypothenus

Sine M = 5√101 / 63

Cos M =?

Adjacent = 38

Hypothenus = 63

Cos M = Adjacent /Hypothenus

Cos M = 38/63

From the calculations made above,

Tan M = 5√101 / 38

Sine M = 5√101 / 63

Cos M = 38/63

Therefore, Option D gives the correct answer.