I need this answer ### Educational Content on Solving Right Triangles#### Problem Description:You are given a right-angled triangle $ \triangle ABC $ with the right angle at $ C $. The length of the side $ BC $ is provided as $ 3 $ units, and the angle $ \angle BAC $ is $ 35^\circ $. The goal is to determine the length of side $ b $, which corresponds to $ AB $.#### Diagram Explanation:- **Vertices**: The triangle has three vertices labeled as $ A $, $ B $, and $ C $.- **Sides**: - $ BC $: Height (vertical side) with a length of $ 3 $ units. - $ CA $: Base (horizontal side). - $ AB $: Hypotenuse, labeled as $ b $.- **Angles**: - $ \angle BCA $: Right angle ($ 90^\circ $). - $ \angle BAC $: $ 35^\circ $.#### Question:What is the value of $ b $?#### Options:1. $ b = 3.28 $2. $ b = 1.28 $3. $ b = 2.28 $4. $ b = 4.28 $#### Solution Approach:To find the length of the hypotenuse $ b $ in a right-angled triangle, we use trigonometric ratios. In this case:\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]Given:- $ \theta = 35^\circ $- Adjacent side $ BC = 3 $We need to find the hypotenuse $ b $:\[ \cos(35^\circ) = \frac{3}{b} \]Rearranging to find $ b $:\[ b = \frac{3}{\cos(35^\circ)} \]By calculating $ \cos(35^\circ) $ and solving for $ b $:\[ b \approx \frac{3}{0.8192} \]\[ b \approx 3.66 \]However, our solution shows that none of the provided options are precisely accurate. Double-check the cosine value and recalculate to ensure the closest numerical match to the provided options.Thus, considering the standard options format and

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Description: I need this answer ### Educational Content on Solving Right Triangles#### Problem Description:You are given a right-angled triangle $ \triangle ABC $ with the right angle at $ C $. The length of the side $ BC $ is provided as $ 3 $ units, and

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Answered: B 3 35 A =? Ob = 3.28 Ob= 1.28 Ob= 2.28…

Math

Geometry

B 3 35 A =? Ob = 3.28 Ob= 1.28 Ob= 2.28 Ob=4.28

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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I need this answer

### Educational Content on Solving Right Triangles

#### Problem Description:
You are given a right-angled triangle $ \triangle ABC $ with the right angle at $ C $. The length of the side $ BC $ is provided as $ 3 $ units, and the angle $ \angle BAC $ is $ 35^\circ $. The goal is to determine the length of side $ b $, which corresponds to $ AB $.

#### Diagram Explanation:
- **Vertices**: The triangle has three vertices labeled as $ A $, $ B $, and $ C $.
- **Sides**:
- $ BC $: Height (vertical side) with a length of $ 3 $ units.
- $ CA $: Base (horizontal side).
- $ AB $: Hypotenuse, labeled as $ b $.
- **Angles**:
- $ \angle BCA $: Right angle ($ 90^\circ $).
- $ \angle BAC $: $ 35^\circ $.

#### Question:
What is the value of $ b $?

#### Options:
1. $ b = 3.28 $
2. $ b = 1.28 $
3. $ b = 2.28 $
4. $ b = 4.28 $

#### Solution Approach:
To find the length of the hypotenuse $ b $ in a right-angled triangle, we use trigonometric ratios. In this case:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Given:
- $ \theta = 35^\circ $
- Adjacent side $ BC = 3 $

We need to find the hypotenuse $ b $:
\[ \cos(35^\circ) = \frac{3}{b} \]

Rearranging to find $ b $:
\[ b = \frac{3}{\cos(35^\circ)} \]

By calculating $ \cos(35^\circ) $ and solving for $ b $:
\[ b \approx \frac{3}{0.8192} \]
\[ b \approx 3.66 \]

However, our solution shows that none of the provided options are precisely accurate. Double-check the cosine value and recalculate to ensure the closest numerical match to the provided options.

Thus, considering the standard options format and

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