Find the value of x, where one side is 9 and the angle is 45 degrees.
Understand the Problem
The question is asking for the length of side x in a right triangle, where one side is 9 units long and an angle is 45 degrees. We will use trigonometric principles to find x.
Answer
$x = 9$
Answer for screen readers
The value of $x$ is $9$.
Steps to Solve
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Identify the triangle sides and angles In a right triangle, we know one angle (45°) and one side (9 units). We need to find the length of side $x$, which is opposite the 45° angle.
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Use the properties of a 45° triangle In a 45°-45°-90° triangle, the two legs are equal in length. Therefore, if one leg's length is 9 units, the other leg (which is $x$) is also 9 units.
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Conclusion Thus, we can express this relationship in the equation: $$ x = 9 $$
The value of $x$ is $9$.
More Information
In a 45°-45°-90° triangle, both legs are of equal length. This property can be very useful in solving problems involving right triangles when the angles are known.
Tips
- Confusing triangle ratios: Ensure you remember that the legs of a 45°-45°-90° triangle are equal.
- Misapplying trigonometric functions: Since the angles are both 45°, special ratios apply rather than standard sine or cosine calculations.
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