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Using Trig to find a side.

Solve for x. Round to the nearest tenth, if necessary.

Using Trig to find a side. Solve for x. Round to the nearest tenth, if necessary.-example-1
User Finley
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Answer:


\large\boxed{\tt x \approx 95.6}

Explanation:


\textsf{We are asked to solve for x by using \underline{Trigonometric Identities}.}


\large\underline{\textsf{What are Trigonometric Identities?}}


\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Trigonometric Identities;}} \\ \\ \textsf{Trigonometric Identities are trigonometric ratios determined with what's given in order to find a missing value. For a Right Triangle, the Trigonometric Identities are Sine, Cosine, and Tangent. These are used to find missing sides.} \\ \\ \tt Sine = \tt $ \tt (Opposite)/(Hypotenuse) \\ \\ Cosine = (Adjacent)/(Hypotenuse) \\ \\ Tangent = (Opposite)/(Adjacent) \end{minipage}}


\textsf{We should determine whether Sine, Cosine, or Tangent will actually help us}


\textsf{determine x. We are given a Right Triangle that has 1 15}^(\circ) \ \textsf{angle, and a side with}


\textsf{a length of 99. Because this side is opposite of the right angle, this side is called}


\textsf{the \underline{Hypotenuse}.}


\textsf{The side labeled x is \underline{Adjacent}, which means that it's touching the given angle.}


\textsf{Using what was given to us, we should use Cosine since we are asked for the}


\textsf{Adjacent Angle when given the Hypotenuse.}


\large\underline{\textsf{Solving;}}


\textsf{Remember that;}


\tt \cos(15^(\circ)) =(Adjacent)/(Hypotenuse)


\textsf{We're given;}


\tt \cos(15^(\circ)) =(x)/(99)


\textsf{To find the value of x, we first should remove the fraction using cancellation.}


\textsf{We are able to use the \underline{Multiplication Property of Equality} to prove that the}


\textsf{equation remains equal.}


\underline{\textsf{Multiply both expressions by 99;}}


\tt 99 \cos(15^(\circ)) =\\ot{99} \frac{x}{\\ot{99}}


\tt 99 \cos(15^(\circ)) =x


\underline{\textsf{Evaluate;}}


\tt 99 \cos(15^(\circ)) \approx \boxed{\tt 95.6}


\large\boxed{\tt x \approx 95.6}

User Eric Huang
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