Certainly! Here is a detailed transcription suitable for an educational website:---**Problem Statement:****1. Find all sides and angles of the following triangles:****a.**A triangle is shown with the following details:- One side is labeled as 11.- The angle opposite this side is 40°.- Another angle is marked as 52°.**b.**A triangle is depicted with the following information:- One side is labeled as 5.- Another side is labeled as 15.- The angle opposite the side labeled 9 is denoted as $ x $.**Explanation:**To solve these problems:- Use the triangle angle sum theorem, which states that the sum of angles in a triangle is 180°.- Apply the Law of Sines or the Law of Cosines as needed to find missing side lengths or angles.For part (a), you can calculate the missing angle since two angles are already given. For part (b), use trigonometric laws to find the unknown angle $ x $ based on the given side lengths.--- This transcription provides a clear description of the problem and guidance on how to approach solving the triangles.

Answered: 1. Find all sides and angles of the…

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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Certainly! Here is a detailed transcription suitable for an educational website:

---

**Problem Statement:**

**1. Find all sides and angles of the following triangles:**

**a.**

A triangle is shown with the following details:

- One side is labeled as 11.
- The angle opposite this side is 40°.
- Another angle is marked as 52°.

**b.**

A triangle is depicted with the following information:

- One side is labeled as 5.
- Another side is labeled as 15.
- The angle opposite the side labeled 9 is denoted as $ x $.

**Explanation:**

To solve these problems:

- Use the triangle angle sum theorem, which states that the sum of angles in a triangle is 180°.
- Apply the Law of Sines or the Law of Cosines as needed to find missing side lengths or angles.

For part (a), you can calculate the missing angle since two angles are already given. For part (b), use trigonometric laws to find the unknown angle $ x $ based on the given side lengths.

---

This transcription provides a clear description of the problem and guidance on how to approach solving the triangles.

Expert Solution

Step 1

Consider the following figure:

Sum of all angles of triangle is $180 °$ .

$\begin{array}{rcl} m ∠ A + m ∠ B + m ∠ C & = & 180 ° \\ m ∠ A + 52 ° + 40 ° & = & 180 ° \\ m ∠ A + 92 ° & = & 180 ° \\ m ∠ A & = & 180 ° - 92 ° \\ m ∠ A & = & 88 ° \end{array}$

Step 2

Use the Sine Rule:

$\begin{array}{rcl} \frac{A C}{\sin B} & = & \frac{A B}{\sin C} \\ \frac{11}{\sin 52 °} & = & \frac{A B}{\sin 40 °} \\ \frac{11}{0.788} & = & \frac{A B}{0.643} \\ A B & = & \frac{11 \times 0.643}{0.788} \\ A B & = & 8.97 \end{array}$

$\begin{array}{rcl} \frac{B C}{\sin A} & = & \frac{A C}{\sin B} \\ \frac{B C}{\sin 88 °} & = & \frac{11}{\sin 52 °} \\ \frac{B C}{0.999} & = & \frac{11}{0.788} \\ B C & = & \frac{11 \times 0.999}{0.788} \\ B C & = & 13.94 \end{array}$

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