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Triangle ABC is a right triangle and sin(53o) = . Solve for x and round to the nearest whole number.

Which equation correctly uses the value of x to represent the cosine of angle A?


cos(53o) = 4/x

cos(53o) = y/5

cos(53o) = x/4

cos(53o) = 5/y

Triangle ABC is a right triangle and sin53o Solve for x and round to the nearest whole number Which equation correctly uses the value of x to represent the cosi class=

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carlosego

To find the value of the variable x, we use the following trigonometric relationship:

[tex] sine (53) = \frac{4}{x}
[/tex]

From here, we clear the value of x.

We have then:

[tex] x = \frac{4}{sine(53)}

x = 5 cm
[/tex]

Then, the cosine of angle A is given by:

[tex] cos (A) = \frac{C.A}{h}
[/tex]

Where,

C.A: adjacent leg

h: hypotenuse

Substituting values we have:

[tex] cos (53) = \frac{y}{5} [/tex]

Answer:

The value of x is:

[tex] x = 5 cm
[/tex]

An equation that correctly uses the value of x is:

[tex] cos (53) = \frac{y}{5} [/tex]

To solve the problem we will use the basic Trigonometric functions.

The value of [tex]Cos(53^o)[/tex] is  [tex]\dfrac{y}{5}[/tex].

What are Trigonometric functions?

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

Given to us

  • AB = x
  • BC = 4 cm
  • AC = y
  • ∠A = 53°

What is the value of x?

In ΔABC,

For ∠A,

[tex]Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin(\angle A)=\dfrac{BC}{AB}\\\\Sin(53^o) =\dfrac{4}{x}\\\\x =\dfrac{4}{Sin(53^o)}\\\\x = 5[/tex]

Value of ∠A

[tex]Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]Cos(\angle A) = \dfrac{AC}{AB}[/tex]

[tex]Cos(53^o) = \dfrac{y}{5}[/tex]

Hence, the value of [tex]Cos(53^o)[/tex] is  [tex]\dfrac{y}{5}[/tex].

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

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