Respuesta :

Answer:

x = 35°

Step-by-step explanation:

Given : [tex]\sin 55^{\circ}=\cos x[/tex]

We have to solve for x.

Consider

[tex]\sin 55^{\circ}=\cos x[/tex]

We know the relation,

[tex]\sin (90^{\circ}-\theta)=\cos \theta[/tex]   .....(1)

also [tex]\sin 55^{\circ}[/tex] can be written as

 [tex]\sin 55^{\circ}=\sin(90^{\circ}-35^{\circ})[/tex]  .....(2)

Comparing the two equations (1) and (2) , we have,

[tex]\sin (90^{\circ}-35^{\circ})=\cos 35^{\circ}[/tex]

Thus, x = 35°

The value of x missing in the box is; x = 35°

Trigonometry

We know that if an angle is x, in trigonometry, we say that;

sin x = cos (90 - x)

Thus;

sin 55 = cos (90 - 55)

sin 55 = cos 35

In conclusion, the missing value as x in the question was gotten to be 35°

Read more on trigonometry at; https://brainly.com/question/13276558

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