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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 sin(53o) = . Solve for x and round to the nearest whole number. Which equation correctly uses the value of x to represent t class=

Verified Answer :

carlosego

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

\(sine (53) = \frac{4}{x}
\)

From here, we clear the value of x.

We have then:

\(x = \frac{4}{sine(53)}

x = 5 cm
\)

Then, the cosine of angle A is given by:


\(cos (A) = \frac{C.A}{h}
\)

Where,

C.A: adjacent leg

h: hypotenuse

Substituting values we have:


\(cos (53) = \frac{y}{5}\)

Answer:

The value of x is:

\(x = 5 cm
\)

An equation that correctly uses the value of x is:

\(cos (53) = \frac{y}{5}\)

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

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

What are Trigonometric functions?

\(Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

\(Cos \theta=\dfrac{Base}{Hypotenuse}\)

\(Tan \theta=\dfrac{Perpendicular}{Base}\)

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,

\(Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\)

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

Value of ∠A

\(Cos \theta=\dfrac{Base}{Hypotenuse}\)

\(Cos(\angle A) = \dfrac{AC}{AB}\)

\(Cos(53^o) = \dfrac{y}{5}\)

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

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

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