Use the Law of Sines to solve the following triangle. Approximate your answers to the nearest tenths. a = 35.0 km, A 13.0° B 65.3⁰ Use the paperclip button below to attach files.
Use the Law of Sines to solve the following triangle. Approximate your answers to the nearest tenths. a = 35.0 km, A 13.0° B 65.3⁰ Use the paperclip button below to attach files.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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# Solving Triangles Using the Law of Sines
In this exercise, we will use the Law of Sines to solve a given triangle. The goal is to approximate the answers to the nearest tenths.
## Given Data
- Angle \( A = 13.0^\circ \)
- Angle \( B = 65.3^\circ \)
- Side \( a = 35.0 \text{ km} \)
## Instructions
To solve for the unknown sides and angles, follow these steps:
### Step 1: Determine the Third Angle
Using the fact that the sum of angles in any triangle is \( 180^\circ \), calculate angle \( C \).
### Step 2: Apply the Law of Sines
The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
### Step 3: Solve for the Unknown Sides
Using the known values, plug into the Law of Sines to find side lengths \( b \) and \( c \).
### Step 4: Approximate to the Nearest Tenths
Round your answers to one decimal place.
---
**Note:**
Students can enter a maximum of 2000 characters in the provided text box.
---
*Student Toolbox:*
- Use the attachment button below to submit any files or additional work related to your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc7859e1-a84c-4143-bc4d-4794151a052e%2F1a018cf3-b455-4bee-90d4-86d200d1a01e%2Fprkyq633_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
# Solving Triangles Using the Law of Sines
In this exercise, we will use the Law of Sines to solve a given triangle. The goal is to approximate the answers to the nearest tenths.
## Given Data
- Angle \( A = 13.0^\circ \)
- Angle \( B = 65.3^\circ \)
- Side \( a = 35.0 \text{ km} \)
## Instructions
To solve for the unknown sides and angles, follow these steps:
### Step 1: Determine the Third Angle
Using the fact that the sum of angles in any triangle is \( 180^\circ \), calculate angle \( C \).
### Step 2: Apply the Law of Sines
The Law of Sines states:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
\]
### Step 3: Solve for the Unknown Sides
Using the known values, plug into the Law of Sines to find side lengths \( b \) and \( c \).
### Step 4: Approximate to the Nearest Tenths
Round your answers to one decimal place.
---
**Note:**
Students can enter a maximum of 2000 characters in the provided text box.
---
*Student Toolbox:*
- Use the attachment button below to submit any files or additional work related to your answer.
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