Question

Find the measure of x

Answer 1

`\large\boxed{\tt x \approx 7.61.}`

Explanation:

`\textsf{For this problem we are asked to find the measure of x.}`

`\textsf{Note that we are given a Right Triangle, which means that we can use one}`

`\textsf{\underline{Trigonometric Identity} to find the value of x.}`

`\textsf{These Trigonometric Identities are Sine, Cosine, and Tangent.}`

`\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{Because we are focused on the 65}^(\circ) \ \textsf{angle, we will use Cosine. Remember that the}`

`\textsf{Hypotenuse is the longest side, and the side opposite from the right angle. The}`

`\textsf{Adjacent Side is the side that the angle is nearest to, or touches. Due to what's}`

`\textsf{given, we have to find x by using cosine.}`

`\large\underline{\textsf{Solving for x;}}`

`\textsf{Let's use cosine to solve for x.}`

`\tt \cos(65^(\circ)) = (x)/(18)`

`\textsf{Cancel out the fraction by using the \underline{Multiplication Property of Equality}, which}`

`\textsf{states that expressions are still equal if they're multiplied by the same term.}`

`\tt 18 * \cos(65^(\circ)) = \frac{\\ot{18}x}{\\ot{18}}`

`\tt 18\cos(65^(\circ)) = x`

`\underline{\textsf{Evaluate;}}`

`\large\boxed{\tt x \approx 7.61.}`