Question

Using a trigonometric ratio to find the angle measure in a right triangle ‼️ round to the nearest tenths‼️

Answer 1

Answer:

x ≈ 43.3°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = $\frac{adjacent}{hypotenuse}$ = $\frac{16}{22}$, thus

x = $cos^{-1}$($\frac{16}{22}$) ≈ 43.3° ( to the nearest tenth )

Answer 2

Answer: 43.3°

Step-by-step 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°