Use the right triangle to answer the question. Which equation can be used to find the value of x? A. x=5.24sin41^circ B x=5.24tan41^circ C. x=(5.24)/(sin41^circ ) D. x=(5.24)/(tan41^circ )

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Use the right triangle to answer the question. Which equation can be used to find the value of x? A. x=5.24sin41^circ B x=5.24tan41^circ C. x=(5.24)/(sin41^circ ) D. x=(5.24)/(tan41^circ )

Answer 1

To find the value of \(x\), which is the length of the left leg of the right triangle, we can use trigonometric ratios. Since we are given the length of the right leg (which is adjacent to the angle) and we need to find the length of the left leg (which is opposite to the angle), we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.The tangent of an angle \(\theta\) in a right triangle is given by:\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]In this case, the angle given is 41°, the opposite side is \(x\), and the adjacent side is 5.24. Therefore, we can set up the equation as follows:\[\tan(41^{\circ}) = \frac{x}{5.24}\]To solve for \(x\), we multiply both sides of the equation by 5.24:\[x = 5.24 \cdot \tan(41^{\circ})\]So the correct equation to find the value of \(x\) is:\[x = 5.24 \tan(41^{\circ})\]The answer is:B. \(x = 5.24 \tan 41^{\circ}\)

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Use the right triangle to answer the question. Which equation can be used to find the value of x? A. x=5.24sin41^circ B x=5.24tan41^circ C. x=(5.24)/(sin41^circ ) D. x=(5.24)/(tan41^circ )

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