Question

Hello I need help with question 16! Solving for X and Y… I will give you a great rating! Please help, I’m not sure how to do this. Also this is not a quiz this is practice. No one is helping me

Answer 1

Given:

To solve for x and y,

Step 1: In ΔABC, Identify the sides of the triangle.

Thus,

`\begin{gathered} AC\Rightarrow hypotenuse\text{ \lparen longest side of the triangle\rparen} \\ BC\Rightarrow opposite\text{ \lparen side facing the angle\rparen} \\ AB\Rightarrow adjacent \end{gathered}`

Step 2: Evaluate x, using trigonometric ratios.

From trigonometric ratios,

`\begin{gathered} \sin\theta=(opposite)/(hypotenuse) \\ \cos\theta=(adjacent)/(hypotenuse) \\ \tan\theta=(opposite)/(adjacent) \end{gathered}`

where θ = 47, we have

`\begin{gathered} \tan\text{ 47 =}(opposite)/(adjacent)=(BC)/(AB) \\ \tan47=(x)/(18) \\ cross-multiply, \\ x=18* tan\text{ 47} \\ =18*1.07236871 \\ \Rightarrow x=19.30263678 \end{gathered}`

Step 4: Evaluate y, using trigonometric ratio.

Thus,

`\begin{gathered} BC\Rightarrow hypotenuse \\ BD\Rightarrow opposite \\ CD\Rightarrow adjacent \end{gathered}`

Step 3: In ΔBCD, identify the sides of the triangle.

Thus,

`\begin{gathered} \cos\theta=(adjacent)/(hypotenuse) \\ where \\ \theta\Rightarrow y \\ adjacent\Rightarrow CD=7 \\ hypotenuse\Rightarrow BC=x \end{gathered}`

Thus, we have

`\begin{gathered} \cos y=(7)/(x) \\ but\text{ } \\ x=19.30263678 \\ thus, \\ \cos y=(7)/(19.30263678) \\ \Rightarrow\cos y=0.3626447557 \\ take\text{ the cosine inverse of both sides,} \\ \cos^(-1)(\cos y)=\cos^(-1)(0.3626447557) \\ \Rightarrow y=68.73729136\degree \end{gathered}`

Hence, the values of x and y are

`\begin{gathered} x=19.30263678 \\ y=68.73729136\degree \end{gathered}`