QQuestionMathematics
QuestionMathematics
In the triangle, what is sin^45∘?
Give your answer in simplest radical form.
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Answer
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Step 1:I'll solve this step-by-step following the specified LaTeX formatting guidelines:
Step 2:: Recall the definition of sine for a 45° angle
The sine of an angle is defined as the ratio of the opposite side to the hypotenuse in a right triangle. For a 45 - 45 - 90 triangle, this has a special geometric interpretation.
Step 3:: Analyze the 45 - 45 - 90 triangle
- If we consider the leg length as 1, the hypotenuse will be $$\sqrt{2}
In a 45 - 45 - 90 triangle: - The two legs are equal in length
Step 4:: Calculate sin(45°)
\sin(45°) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{\sqrt{2}}
Step 5:: Simplify the radical
\sin(45°) = \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}
Final Answer
\sin(45°) = \frac{\sqrt{2}}{2}
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