To determine the length of the side \(b\) using the information you provided (an angle of \(27^\circ\) and a side length of \(5.0 , \text{cm}\)), we need more context. Is this a right triangle, or do you have another side or angle that we need to consider?
Assuming we have a right triangle where:
- \(27^\circ\) is one of the angles,
- \(5.0 , \text{cm}\) is the length of the adjacent side to the angle, and we want to find the length of the opposite side \(b\).
Using the tangent function: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] we can rearrange this to find the length of the opposite side \(b\): \[ b = \tan(27^\circ) \times 5.0 , \text{cm} \]
Now we can calculate \(b\):
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Find \(\tan(27^\circ)\) using a scientific calculator or table. This gives approximately: \[ \tan(27^\circ) \approx 0.5095 \]
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Now, calculate \(b\): \[ b \approx 0.5095 \times 5.0 \approx 2.5475 , \text{cm} \]
Rounding to the nearest tenth of a centimeter: \[ b \approx 2.5 , \text{cm} \]
If you meant something different (like looking for a different side or angle), please provide more details!
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