Find the value of x in the triangle. Round to the nearest tenth as needed.
Understand the Problem
The question asks to find the value of 'x' in the given right triangle. We are given the hypotenuse (540 yd) and an angle (36 degrees). We can use trigonometric functions (specifically the sine function) to find 'x', which is the side opposite to the given angle. Finally, we need to round the answer to the nearest tenth.
Answer
$ x = 317.4 $
Answer for screen readers
$ x = 317.4 $
Steps to Solve
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Identify the trigonometric ratio Since we are given the hypotenuse and the angle, and we need to find the side opposite to the angle, we use the sine function: $ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} $
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Write the equation using the given values Substitute the given angle $ \theta = 36^\circ $ and the hypotenuse $= 540$ yd into the sine equation: $ \sin(36^\circ) = \frac{x}{540} $
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Solve for x Multiply both sides of the equation by 540 to isolate $x$: $ x = 540 \cdot \sin(36^\circ) $
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Calculate the value of x Using a calculator, find the value of $ \sin(36^\circ) \approx 0.587785252 $ $ x = 540 \cdot 0.587785252 \approx 317.403036 $
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Round to the nearest tenth Round the value of $x$ to the nearest tenth: $ x \approx 317.4 $
$ x = 317.4 $
More Information
The value of $x$ represents the length of the side opposite the $36^\circ$ angle in the given right triangle.
Tips
A common mistake is using the wrong trigonometric function (e.g., cosine or tangent) or incorrectly setting up the ratio. Also, make sure your calculator is in degree mode when calculating the sine of the angle. Forgetting to round to the nearest tenth as instructed can also be a mistake.
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