gavinperkins
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Which equation can be solved to find one of the missing side lengths in the triangle? Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units. cos(60o) = StartFraction 12 Over a EndFraction cos(60o) = StartFraction 12 Over b EndFraction cos(60o) = StartFraction b Over a EndFraction cos(60o) = StartFraction a Over 12 EndFraction

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joseaaronlara

Answer:

The answer to your question is: letter D, last option

Step-by-step explanation:

Data

Triangle  ABC

∠C = 90°

∠B = 60°

CB = a

CA = b

hypotenuse (AB) = 12 units

Options

a) cos 60 = [tex]\frac{12}{a}[/tex]   this equation is calculating secФ

b) cos 60 = [tex]\frac{12}{b}[/tex]  this equation is determining csc Ф

c) cos 60 = [tex]\frac{b}{a}[/tex]     this equation is determaning tanФ

d) cos 60 = [tex]\frac{a}{12}[/tex]   this equation is determining cosФ,  so

                                                       this is the correct answer

The cosine of an angle is equal to the ratio of the base to the hypotenuse. The correct option is given by D) and this can be determined by using the trigonometry functions.

Given :

  • Triangle ABC
  • [tex]\rm \angle ACB = 90^\circ[/tex]
  • [tex]\rm \angle CBA = 60^\circ[/tex]
  • Length of side CB = a
  • Length of side CA = b
  • Length of Hypotenuse AB = 12

The cosine function is one of the important trigonometric functions. The cosine of an angle is equal to the ratio of the base to the hypotenuse.

The mathematical expression of cosine is given by:

[tex]\rm cos\theta = \dfrac{B}{H}[/tex]      ----- (1)

where B is the base and H is the hypotenuse.

Now, put the value of [tex]\theta[/tex], B, and H in equation (1).

[tex]\rm cos60^\circ = \dfrac{CB}{AB}[/tex]

[tex]\rm cos 60^\circ = \dfrac{a}{12}[/tex]

Therefore, the correct option is given by D).

For more information, refer to the link given below:

https://brainly.com/question/10283811