Question

In AABC it is given that: ADBC, B = 60.5°, AD 18.2 cm and DC 9.7 cm. Calculate the following (remember to round answers off to two decimal spaces): 3.1 AC​

Answer 1

In
`\displaystyle\sf AABC`, it is given that:
`\displaystyle\sf ADBC, \angle B = 60.5^\circ`,
`\displaystyle\sf AD = 18.2` cm, and
`\displaystyle\sf DC = 9.7` cm. We need to calculate the length of
`\displaystyle\sf AC`.

To solve this, we can use the Law of Cosines, which states:

`\displaystyle\sf c^(2) = a^(2) + b^(2) - 2ab \cdot \cos(C)`

In our case, we have:

`\displaystyle\sf AC^(2) = AD^(2) + DC^(2) - 2 \cdot AD \cdot DC \cdot \cos(B)`

Substituting the given values:

`\displaystyle\sf AC^(2) = 18.2^(2) + 9.7^(2) - 2 \cdot 18.2 \cdot 9.7 \cdot \cos(60.5^\circ)`

Now we can calculate
`\displaystyle\sf AC`:

`\displaystyle\sf AC = \sqrt{AC^(2)}`

Using a calculator or a mathematical software, we find that:

`\displaystyle\sf AC \approx 20.10` cm

Therefore, the length of
`\displaystyle\sf AC` is approximately
`\displaystyle\sf 20.10` cm.