Question

Find CD.
7.5
D
C
E
69°
Write your answer as an integer or as a decimal rounded to the nearest tenth.
CD =

Answer 1

To find the length of side CD, we can use the Law of Sines, which relates the ratio of lengths of sides of a triangle to the sines of their opposite angles.

Given the information:
- Side DE = 7.5
- Angle E = 69°
- We'll denote angle D as \(\angle D\) and angle C as \(\angle C\).

To use the Law of Sines, we also need to know either angle D or angle C to proceed. However, this information is not explicitly provided, so we'll define angle D in terms of angle C as follows:

1. **Assuming we had all angles:**
Since we don’t have additional information for angles, consider if angle D or angle C can be calculated if we had a triangle (let’s call it triangle CDE).

For example, let’s say angle C is labeled but was not provided:
- If we knew angle C too or the relationship between angles in a triangle (triangle sum theorem states that the sum of the angles in triangle is 180°), we could express:
\[
angle C = 180° - (69° + angle D)
\]

2. **Using Law of Sines:**
The Law of Sines formula would look like this:
\[
\frac{CD}{\sin E} = \frac{DE}{\sin D} \rightarrow \frac{CD}{\sin(69°)} = \frac{7.5}{\sin(D)}
\]
Rearranging gives:
\[
CD = \frac{7.5 \sin(69°)}{\sin(D)}
\]

However, without a specific angle (which angle D is), we are unable to directly compute CD.

Given the lack of details about angle C or D, you're unable to determine CD as we lacked information for solving this triangle definitively. If you have any additional details regarding side lengths or angles, please provide them to find CD accurately!