Question

Using Trig to find a side.

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

Answer 1

`\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}`