Answer:
Option D. Cos M = 38/63
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.