Question
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
Remaining Attempts : 3
one side 20 degrees
second side 30 degrees
Remaining Attempts : 3
one side 20 degrees
second side 30 degrees
Answers
GPT-4o mini
To find the unknown side length in a triangle given two angles, we can use the fact that the sum of the angles in any triangle is always 180 degrees. From the information you've provided, you have angles of 20 degrees and 30 degrees.
1. **Calculate the third angle:**
\[
\text{Third angle} = 180^\circ - 20^\circ - 30^\circ = 130^\circ
\]
2. At this stage, we have a triangle with angles of 20 degrees, 30 degrees, and 130 degrees. To find the unknown side length, we would also need to know at least one side length of the triangle. If we assume that the side opposite the 20-degree angle is known, we can apply the Law of Sines.
The Law of Sines states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
where:
- \(a\) is the side opposite angle \(A\),
- \(b\) is the side opposite angle \(B\),
- \(c\) is the side opposite angle \(C\).
If you can provide any side length, we can find the unknown side.
1. **Calculate the third angle:**
\[
\text{Third angle} = 180^\circ - 20^\circ - 30^\circ = 130^\circ
\]
2. At this stage, we have a triangle with angles of 20 degrees, 30 degrees, and 130 degrees. To find the unknown side length, we would also need to know at least one side length of the triangle. If we assume that the side opposite the 20-degree angle is known, we can apply the Law of Sines.
The Law of Sines states:
\[
\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}
\]
where:
- \(a\) is the side opposite angle \(A\),
- \(b\) is the side opposite angle \(B\),
- \(c\) is the side opposite angle \(C\).
If you can provide any side length, we can find the unknown side.