Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place.)

*a* = 28,    *c* = 44,    ∠*A* = 129°

To solve for all possible triangles using the Law of Sines with the given conditions, we have:

- \( a = 28 \)
- \( c = 44 \)
- \( \angle A = 129^\circ \)

The Law of Sines states:

\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]

### Step 1: Solve for \( \angle C \)
We can use the Law of Sines to solve for \( \angle C \) first. Rearranging the formula for \( \sin C \), we get:

\[
\frac{a}{\sin A} = \frac{c}{\sin C} \implies \sin C = \frac{c \cdot \sin A}{a}
\]

Substitute the known values:

\[
\sin C = \frac{44 \cdot \sin 129^\circ}{28}
\]

First, compute \( \sin 129^\circ \):

\[
\sin 129^\circ \approx 0.7431
\]

Now substitute:

\[
\sin C = \frac{44 \cdot 0.7431}{28} = \frac{32.6964}{28} \approx 1.1677
\]

### Step 2: Analyze \( \sin C \)
Since \( \sin C \) cannot be greater than 1, this indicates that no valid triangle exists with the given conditions.

Thus, the solution is:

\[
\boxed{\text{DNE}}
\]

### Would you like more details, or do you have any questions?

---

Here are 5 related questions for practice:

1. What is the Law of Sines used for in triangle problems?
2. Solve for an angle in a triangle given two sides and one angle.
3. What is the Law of Cosines, and how does it differ from the Law of Sines?
4. Can a triangle exist if one of its angles is greater than 180°?
5. How do you find the area of a triangle using trigonometry?

**Tip:** If you get an impossible sine value (greater than 1 or less than -1), it usually means that no triangle exists under the given conditions.

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 28, c = 44, ∠A = 129°

Solve the triangle with sides a = 28, c = 44, and angle A = 129° using the Law of Sines. This problem demonstrates how to apply trigonometric formulas to determine if a valid triangle exists. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation