To find the approximate angle formed at the base of the triangle after cutting a piece of cardstock paper that measures 5 inches in height (h) and has a base of 3.5 inches (b), we can use trigonometry.
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Understand the triangle:
- The height (h) is 5 inches.
- The base (b) is 3.5 inches.
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Determine the angle at the base: We can consider one of the two right triangles formed by the height of the triangle. The base of the right triangle would be half of the original base (since it is cut vertically), which would be \( \frac{3.5}{2} = 1.75 \) inches.
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Use the tangent function: The tangent of the angle (let's call it θ) can be calculated using the formula:
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\text{half of the base}} = \frac{5}{1.75} \]
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Calculate θ: \[ \tan(θ) ≈ \frac{5}{1.75} ≈ 2.857 \]
To find angle θ, take the arctangent (inverse tangent):
\[ θ = \tan^{-1}(2.857) \approx 70° \]
Since we want one of the base angles of the original triangle, let's consider the one that corresponds to the 5-inch height and 1.75-inch base.
This would give us one of the angles at the base of the triangle.
To summarize the angles:
- The complete triangle has angles comprising the apex formed by the height and the two base angles. As we can see, the base angles will not likely reach the upper side of 70 degrees.
- Since the opposite angle formed would factor in, and using common angles might yield:
So calculating and analyzing all angles formed leads that none surprisingly fit. Out of the choices given (55°, 45°, 65°, 35°), the closest approximate angle seems to be around 65°.
Thus, the approximate angle formed at the base of the triangle is 65°.
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