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

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,

$\begin{gathered} \sin\theta=\frac{opposite}{hypotenuse} \\ \cos\theta=\frac{adjacent}{hypotenuse} \\ \tan\theta=\frac{opposite}{adjacent} \end{gathered}$

where θ = 47, we have

$\begin{gathered} \tan\text{ 47 =}\frac{opposite}{adjacent}=\frac{BC}{AB} \\ \tan47=\frac{x}{18} \\ cross-multiply, \\ x=18\times tan\text{ 47} \\ =18\times1.07236871 \\ \Rightarrow x=19.30263678 \end{gathered}$

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,

$\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ where \\ \theta\Rightarrow y \\ adjacent\Rightarrow CD=7 \\ hypotenuse\Rightarrow BC=x \end{gathered}$

Thus, we have

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

Hence, the values of x and y are

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