To find the angle at the base of the triangle formed by cutting the cardstock paper diagonally, we can use the dimensions provided:
- Height (h) = 5 inches
- Base (b) = 3.5 inches
In a right triangle where the height is the vertical side and half of the base is the horizontal side, we can first calculate half of the base:
\[ \text{Half the base} = \frac{b}{2} = \frac{3.5}{2} = 1.75 \text{ inches} \]
Now we can identify the triangle formed when cut diagonally. To find the angle (let's denote it as θ) at the base, we can use the tangent function:
\[ \tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{\text{Half the base}} = \frac{5}{1.75} \]
Calculating this gives:
\[ \tan(θ) \approx \frac{5}{1.75} \approx 2.8571 \]
Now we need to find the angle whose tangent is approximately 2.8571. We can do this by using the arctangent function:
\[ θ = \tan^{-1}(2.8571) \]
Calculating the arctangent will give us an approximate value. Using a calculator:
\[ θ \approx 70.7° \]
However, since we know that there are multiple options given for base angles, let’s also consider angle calculations in a triangle setup.
If we consider that in a triangle, the sum of the angles is 180°, and the right triangle represents a 90° angle, we can take angles off of that. The angle we are looking for (at base) would be:
\[ \text{Base Angle} \approx 90° - θ \]
Since θ = 70.7°, the base angle would be approximately:
\[ 90° - 70.7° \approx 19.3° \]
It doesn’t directly match the given options, therefore we will need to assess the closest angle formed:
Considering the standard approximate options presented are 65°, 35°, 45°, and 55°, we see that 65° is the nearest option calculated based on the triangle's appearance since the remaining angles would all have a larger tendency to close the base.
Thus, the most appropriate angle at the base of the triangle formed when cutting the cardstock is:
65°.
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