Questions: Solve for x. Round to the nearest tenth, if necessary.

Solve for x. Round to the nearest tenth, if necessary.
Transcript text: Solve for $x$. Round to the nearest tenth, if necessary.
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Solution

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Solution Steps

Step 1: Identify the given information

We are given a right triangle NPO, with angle P measuring 69 degrees, side PO measuring 80 units, and side NO labeled as _x_. We are asked to solve for _x_.

Step 2: Choose the appropriate trigonometric ratio

Since we are given the angle P and the side adjacent to it (PO), and we need to find the side opposite to it (NO), we will use the tangent function. The tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle.

Step 3: Set up the equation

Using the tangent function, we can set up the equation: \\(\tan(69^\circ) = \frac{NO}{PO} = \frac{x}{80}\\)

Step 4: Solve for x

Multiply both sides of the equation by 80 to isolate x: \\(x = 80 \times \tan(69^\circ)\\) \\(x \approx 80 \times 2.605\\) \\(x \approx 208.4\\)

Final Answer:

\\(\boxed{x \approx 208.4}\\)

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