Use the Law of Sines to solve the triangle. Round your answers to two decimal places.
B = 31°,  C = 97°,  a = 3
5
8


To solve the triangle using the Law of Sines, we first need to find the remaining angle \( A \), and then use the Law of Sines formula to find the sides \( b \) and \( c \).

### Step 1: Find Angle \( A \)

The sum of the angles in a triangle is always \( 180^\circ \):
\[
A + B + C = 180^\circ
\]
Substituting the known values:
\[
A + 31^\circ + 97^\circ = 180^\circ
\]
\[
A = 180^\circ - 31^\circ - 97^\circ = 52^\circ
\]

So, \( A = 52^\circ \).

### Step 2: Apply the Law of Sines

The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
Given \( a = 3 \), \( A = 52^\circ \), \( B = 31^\circ \), and \( C = 97^\circ \), we can find \( b \) and \( c \).

#### Find \( b \)
\[
\frac{3}{\sin 52

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. B = 31°, C = 97°, a = 3

Learn how to solve a triangle with angles B = 31°, C = 97°, and side a = 3 using the Law of Sines. This step-by-step solution covers important trigonometric concepts such as the Law of Sines and the sum of angles in a triangle. 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