Question

Solve for xx. Round to the nearest tenth, if necessary.
Q
R
S
64°
x
2.8
Answer
Attempt 2 out of 2

x, equalsx=
and 2.5 is not and answer remember x is the longest side

Answer 1

r has a right angle

Answer 2

To solve for \( x \) in a triangle with given angles and side lengths, we can use the Law of Sines or the Law of Cosines. However, since we need to determine the longest side, we'll follow these steps assuming triangle \( QRS \) has the following details:

- \( \angle Q = 64^\circ \)
- \( \angle R = x \)
- \( \angle S \) can be computed since the sum of all angles in a triangle equals \( 180^\circ \).
- One side known: \( RS = 2.8 \)

1. **Finding Angle S**:

Set \( \angle S \) as \( S \):
\[
S = 180^\circ - Q - R
\]
\[
S = 180^\circ - 64^\circ - x
\]

2. **Using the Law of Sines**:

The Law of Sines states that:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Using this law to find side \( QS \) (which is \( x \)), we can denote:
- \( a = QS = x \)
- \( b = RS = 2.8 \)

So we have:
\[
\frac{x}{\sin S} = \frac{2.8}{\sin Q}
\]

Substitute known values:
\[
\frac{x}{\sin(180^\circ - 64^\circ - x)} = \frac{2.8}{\sin(64^\circ)}
\]

But since \( \sin(180^\circ - \theta) = \sin(\theta) \), we can simplify it, but we need the exact value of \( S \) to find \( x \).

3. **Finding \( x \)**:

As per the scenario, let's assume we know \( R \) by checking that \( x \) should be more than \( 2.8 \) (since you said \( x \) is the longest side). The only constraint for \( x \) is that it must be greater than \( 2.8 \).

Given that you'll want to check it against possible angles, you’ll need to confirm the range of valid angles \( R \) to find the valid \( x \).

If \( R \) is defined strictly, substitute and compute via the sine law and ensure check:

1. Iterate possible values for \( x \) given the constraints.
2. Ensure result falls within the triangle inequality constraints for validation.

Due to missing explicit values for angle \( R \), further specificity for precision is limited. If provided those values, we could calculate the precise \( x \).

In conclusion: please confirm the angle \( x \) or recheck its boundaries for accurate solution findings. The possible value can come from iterations of cosine law or sine law constrained by angle validations.

For a direct numeric estimation, reevaluate angles to determine potential values for \( x \) to compare options.