**Title: Calculating the Length of a Triangle Side Using the Law of Cosines****Problem Statement:**Consider the triangle shown below where $ \angle C = 53^\circ $, $ b = 10 \text{ cm} $, and $ a = 24 \text{ cm} $. **Diagram Description:**- The triangle is labeled with points $ A $, $ B $, and $ C $.- Angle $ \angle C $ is $ 53^\circ $.- Side $ AC $ is $ 10 \text{ cm} $.- Side $ BC $ is $ 24 \text{ cm} $.- Side $ AB $ is $ x $ cm (to be determined).``` C / \ 53°/ \ 24 cm / \A /________B 10 cm x cm```**Task:**Use the Law of Cosines to determine the value of $ x $ (the length of $ AB $ in cm).**Input Section:**```x = [ ]```**[Preview] Button****Useful Link:**[Statement of the Law of Cosines](insert_link_here)**Submission Button:**```[Submit]```**Instructions:**1. Substitute the given values into the Law of Cosines formula:\[ x^2 = a^2 + b^2 - 2ab \cos(C) \]2. Given: - $ a = 24 \text{ cm} $ - $ b = 10 \text{ cm} $ - $ \angle C = 53^\circ $3. Calculate the value of $ x $:\[ x = \sqrt{24^2 + 10^2 - 2 \cdot 24 \cdot 10 \cdot \cos(53^\circ)} \]4. Enter your value for $ x $ in the provided input box and click "Preview" to check your answer.5. Once reviewed, click "Submit" to finalize your answer.

Given: a = 24cm, b = 10cm, measure of angle C is 53 degrees. To find: The value of x, by using…

Consider the triangle shown below where m2C = 53°, b = 10 cm, and a = 24 cm. 53 24 cm 10 cm A х ст Use the Law of Cosines to determine the value of x (the length of AB in cm). Preview Statement of the Law of Cosines.

Consider the triangle shown below where m2C = 53°, b = 10 cm, and a = 24 cm. 53 24 cm 10 cm A х ст Use the Law of Cosines to determine the value of x (the length of AB in cm). Preview Statement of the Law of Cosines.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 19E: Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of...

See similar textbooks

Related questions

Q: A temporary support for an architectural feature is positioned 2 feet away from a wall and forms…

A: Use height and distant concept

Q: A man who is 2 m tall stands on horizontal ground 30 m from a tree. The angle of elevation of the…

Q: Elijah helped a young lady up the wheelchair ramp. The base of the ramp is 198 inches long. The…

A: The situation is represented in the following figure. The length of the base of the ramp be BC=198…

Q: Triangle ABC is a non-right triangle. Find angle A, where a 13.2 cm, c-24.6 cm and <C- 52°.

A: To find angle of a non right angled triangle we use "Laws of sin" as given below

Q: 10 feet

A: Cosx=base/hypotenuse

Q: Solve the triangle using the Law of Sines. (Assume a = 6.5, b = 3.7, and LA = 80°. Round the length…

A: Given, a=6.5, b=3.7 & ∠A=80°. We have to find c, ∠B & ∠C using Law of sines.

Q: Which triangle is a 30°-60°-90° triangle?

Q: Solve the right triangle ABC, where C = 90°. a=77.2 yd, b=40.6 yd

A: The tangent of an acute angle in an right triangle is defined as the ratio of length of the side…

Q: Classify the triangle by its angles and by its sides 1. 68° 2. 19° 19° 60° 22° 60%

Q: Find the side c in a triangle ABC, if angles A= 66°, C = 56°, and side b= 12 cm. O 0.70 cm O 0.98 cm…

A: From the given problem the representative diagram is shown below: Let the side c=xcm From the…

Q: 1. Derive the law of sines using the triangle shown below. Suggestion: Try writing the length of the…

Q: Triangle ABC is shown below with all three side lengths known. В 15 cm 11.2 cm C A 22.8 cm

Q: While fishing on a lake, the fisherman looks up at a cliff. His boat is 35 ft. from the base of the…

Q: angle b. solve triangle

A: Given: To determine: Angle B.

Question

**Title: Calculating the Length of a Triangle Side Using the Law of Cosines**

**Problem Statement:**

Consider the triangle shown below where $ \angle C = 53^\circ $, $ b = 10 \text{ cm} $, and $ a = 24 \text{ cm} $.

**Diagram Description:**

- The triangle is labeled with points $ A $, $ B $, and $ C $.
- Angle $ \angle C $ is $ 53^\circ $.
- Side $ AC $ is $ 10 \text{ cm} $.
- Side $ BC $ is $ 24 \text{ cm} $.
- Side $ AB $ is $ x $ cm (to be determined).

```
C
/ \
53°/ \ 24 cm
/ \
A /________B
10 cm x cm
```

**Task:**

Use the Law of Cosines to determine the value of $ x $ (the length of $ AB $ in cm).

**Input Section:**
```
x = [ ]
```
**[Preview] Button**

**Useful Link:**

[Statement of the Law of Cosines](insert_link_here)

**Submission Button:**

```
[Submit]
```

**Instructions:**

1. Substitute the given values into the Law of Cosines formula:
\[ x^2 = a^2 + b^2 - 2ab \cos(C) \]

2. Given:
- $ a = 24 \text{ cm} $
- $ b = 10 \text{ cm} $
- $ \angle C = 53^\circ $

3. Calculate the value of $ x $:
\[ x = \sqrt{24^2 + 10^2 - 2 \cdot 24 \cdot 10 \cdot \cos(53^\circ)} \]

4. Enter your value for $ x $ in the provided input box and click "Preview" to check your answer.

5. Once reviewed, click "Submit" to finalize your answer.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

Use the analytic method to decide what type of triangle is formed when the midpoints of the sides of an isosceles triangle are joined by line segments.
Write a G-code program for the counterclockwise arc with starting point (-40, -20), ending point (30, -90), and center at (80, 30), where units are in millimeters.
Triangle A'B'C" is created by dilating triangle 4. What is the length of A" B"?
how do i solve this?
How to measure angles using a protractor
The side lengths of a triangle are 6, 8, and 12. Is this a right triangle? A. No, because 6 + 8= 12 B. Yes, because 6^2 + 8^2 < 12^2 C. Yes, because 6^2 + 8^2 = 12^2 D. No, because 6^2 +8^2 = 12^2
A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water? *please use handwriting not type, I understand it better that way*
Complete the dimensions of the given triangle
a right triangle has coordinates (-3, 4) (3, 6) and (-1, -2). what is the area of the right triangle?
tion 1 2 3 4 5 6 7 8 9 ~ Construct a problem where a student needs to find the missing measure of a triangle using the midsegment equation. Provide a labeled triangle, solution and steps for solving the problem. Save
Which triangle is similar to triangle XYZ?
how can i find a length of a right triangle only using 1 side and an angle