Answer: 43.3°
Explanation:
From the trigonometric ratio, there are three basic identities
(1) SOH, meaning
Sine = Opposite all over the hypothenus, opposite side is always the side that faces the define or the indicated angle in the right angled triangle.
Sine = opp/hyp.
(2) CAH meaning
Cosine = Adjacent side all over the hypothenus, adjacent side is the sisde that is opposite the undefined or unindicated side of the right angled triangle.
(3) TOA meaning
Tangent = Opposite side all over the adjacent, note that the hypothenus side is the longest side which connects both the opposite and the adjacent sides of the right angled triangle.
Note that trigonometric ratio is only applicable in solving angles taht are right angles.
Now , back to the question, from the diagram,the side that is facing the indicated angle ( X° ) is the opposite side while the one facing the un-indicated angle is the adjacent which is ( 16 ) while the hypothenus is (22)
To consider which of the ratio above is applicable, we consider the relationship between the 3
Here now, we were given the adjacent and the hypothenus, therefore number two will be appropriate because it is only cosine that connect the two sides together.
Now,
Cosx° = 16/22
= 0.7272727272
Now approximate to four figures
0.7273
Since we are looking for x°
x° = 1/cos0.7273
= but it is a mathematical blunder to divide anything by the functions, cos, sine, tan, we now recall the laws' of indicies
1/a = a^-1 , therefore
1/cos0.7273 = cos^-1 0.7273 which is also known as the inverse of cos
checking this in your log tables or calculator by pressing the shift and inverse function of cos0,7273 gives you
cos^-1 0,7273 = 43.3
= 43.3°
x = 43.3°