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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

Hello I need help with question 16! Solving for X and Y… I will give you a great rating-example-1
User Topched
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Solution:

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}

Hello I need help with question 16! Solving for X and Y… I will give you a great rating-example-1
User Lanre
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