Could someone help me with this trigonometry question where you have to calculate the length of bc, to the nearest degree.

The length of BC ≈ 12.4 cm

Step-by-step explanation:

The first thing we need to do is to find the length of BD which we can solve for with the tangent of 20° which is the opposite side over the adjacent side.

We get tan20° = BD/8.

Solve for BD and you get BD = 8tan20°.

Now we will need to solve for the length of CD which we can get from the tangent of 40°.

We get tan40° = 8/CD

Solve for CD and you get CD = 8/tan40°.

Now that we have the lengths of BD and DC, we can simply add them together to get the length of BC.

(8tan20°) + (8/tan40°) ≈ 12.4 cm