Questions: Solve the right triangle for the x and y using soh cah toa

Solve the right triangle for the x and y using soh cah toa
Transcript text: *Solve the right triangle for the $x$ and $y$ using soh cah toa (2)
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Solution

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Solution Steps

Step 1: Find y in the first triangle using Cosine

We are given the hypotenuse (22) and the angle (37°), and we need to find the adjacent side (y). Therefore, we use cosine:

\\(\cos(37^\circ) = \frac{y}{22}\\) \\(y = 22 \cos(37^\circ)\\) \\(y \approx 22 \times 0.7986\\) \\(y \approx 17.57\\)

Step 2: Find x in the first triangle using Sine

We are given the hypotenuse (22) and the angle (37°), and we need to find the opposite side (x). Therefore, we use sine:

\\(\sin(37^\circ) = \frac{x}{22}\\) \\(x = 22 \sin(37^\circ)\\) \\(x \approx 22 \times 0.6018\\) \\(x \approx 13.24\\)

Step 3: Find y in the second triangle using Sine

We are given the opposite side (18) and the angle (33°), and we need to find the hypotenuse (y). Therefore we use sine: \\(\sin(33^\circ) = \frac{18}{y}\\) \\(y = \frac{18}{\sin(33^\circ)}\\) \\(y \approx \frac{18}{0.5446}\\) \\(y \approx 33.05\\)

Final Answer

\\(\boxed{1. \ x \approx 13.24, y \approx 17.57} \\) \\(\boxed{2. \ y \approx 33.05}\\)

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