Question

determine the length of each indicated side to the nearest tenth of a centimetre
a. 27degrees, 5.0cm, b

Answer 1

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 \(b\):
1. Find \(\tan(27^\circ)\) using a scientific calculator or table. This gives approximately:
\[
\tan(27^\circ) \approx 0.5095
\]

2. 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!