### Identifying True Statements in a Scalene TriangleConsider the right-angled triangle $ \Delta CAB $ shown in the diagram. For this triangle:- $ \angle CAB $ is represented by $ \alpha $- $ \angle CBA $ (the right angle)- $ \angle ADB $ is represented by $ \beta $The triangle has sides labeled as follows:- Side $ a $ opposite angle $ \alpha $- Side $ b $ adjacent to angle $ \alpha $- Hypotenuse $ c $### Problem StatementIdentify ALL of the following statements that are true in the given $ \Delta CAB $ where $ \alpha + \beta = 90^\circ $: (1 point)- **A.** $ \sin(\beta) = \cos(\alpha) $- **B.** $ \tan(\beta) = \tan(\alpha) $- **C.** $ \cos(\beta) = \sin(\alpha) $- **D.** $ \cos(\beta) = \sin(90^\circ - \alpha) $**Answer Options:**- ☐ A- ☐ B- ☐ C- ☐ D### Diagram ExplanationThe diagram provided is a right-angled triangle labeled $ \Delta CAB $:- $ \angle CBA = 90^\circ $- $ \angle CAB = \alpha $- $ \angle ADB = \beta $- Side opposite $ \alpha $ is $ a $- Side adjacent to $ \alpha $ is $ b $- Hypotenuse is $ c $### Analysis of Statements- **Statement A:** $ \sin(\beta) = \cos(\alpha) $ - By trigonometric identity in a right triangle, this is true because $ \beta = 90^\circ - \alpha $. Therefore, $ \sin(\beta) = \sin(90^\circ - \alpha) = \cos(\alpha) $.- **Statement B:** $ \tan(\beta) = \tan(\alpha) $ - This is false. $ \tan(\beta) = \tan(90^\circ - \alpha) = \cot(\alpha) $. Therefore, \( \tan(\beta) \neq \tan(\alpha)

Name: ### Identifying True Statements in a Scalene TriangleConsider the rig
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: ### Identifying True Statements in a Scalene TriangleConsider the right-angled triangle $ \Delta CAB $ shown in the diagram. For this triangle:- $ \angle CAB $ is represented by $ \alpha $- $ \angle CBA $ (the right angle)- $ \angle ADB $

Answered: Image /qna-images/answer/96206173-a64d-449a-8580-d9c2e8ca99c9.jpg

Math

Geometry

Rectangular Snip Identify ALL of the following statements that are true in the diagram if ACAB is a scalene triangle. (1 point) в O A. sin(B) = cos(a) O B. tan(B) = tan(a) %3D O C. cos (B) = sin (a) O D. cos(B) = sin(90 – a) A b A

Rectangular Snip Identify ALL of the following statements that are true in the diagram if ACAB is a scalene triangle. (1 point) в O A. sin(B) = cos(a) O B. tan(B) = tan(a) %3D O C. cos (B) = sin (a) O D. cos(B) = sin(90 – a) A b A

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

See similar textbooks

Related questions

Q: sec a sec B tan B The expression tan a (wherever defined) can take the value- (A) 4 (B) 6 (C) S (D)…

Q: 3 sin B =- 5 5 0< A<- 13 Зл find the following: 3. If cos A = and t <B<- a. cos(A+B) b. sin(A+B)

A: topic - trigonometric identities cos(A+B)=cosAcosB-sinAsinB

Q: 2. Find sin(A) and tan(B) using the right triangle below. B 11 6

Q: 1. Draw the angle, mark reference angle, and find the exact value (for a and b) (a) sin(-210 (b)…

A: To draw and find angles

Q: |17 Suppose that sin a + sin b = and cos a + cos b= 1. What is cos(a – b)? (A) V – 1 (B) (C) 를 (D)를…

A: Given that, sina+sinb=53 (1)cosa+cosb=1 (2)

Q: Task 2: A common mistake when learning about sines and cosines is to assert sin(x + y) = sin(x)+…

A: To show the given statement is not true, take x=30⁰ and y=60⁰. Therefore (x+y)=90⁰.

Q: 3 Let cot (0) = and sec(0) < 0. 4 - a. Place U in a coordinate system in correct quadrant and solve…

A: (a) Here, cot θ=34⇒cos θsin θ=34 Now, sec θ<0⇒cos θ<0 is given but cot θ>0. So, tan θ is…

Q: The right triangle below satisfies 0 cos(B) tan(0) = tan(B) sin(ß) < tan(ß) D sin(B) < cos(0) a O E…

Q: S COSA Sin 2X. C dx

A: We have to find integration

Q: Let a and B be first quadrant angles with cos(a) = V3 and sin(B) V10 5 Find cos(a - B).

Q: C 25 7 T

Q: ( cos rdx = CO Select one: a. x sin2x +c 2 b. * sin2r 41 sin2r 41 C. sin21 C d. a +. 21

Q: An angle's initial ray points in the 3-o'clock direction and the angle measures radians. Which of…

A: It is given that an angle's initial ray points is in the 3-o'clock direction.

Q: Consider the angle t defined by on the unit circle. y TO IND (3) I

A: Consider the angle t defined by the point 35, 45 on the unit circle. To Find:1 sint=?2 cost=?3…

Q: Cos a is? Tan a is?

Q: 3. Đ 4. 15 20

Q: Calculate / cot cot³(x) csc³(x) dx. Your answer should be in terms of x.

Q: Q3 Find the value of the angle of cos(sin (x)) ?

A: The given trigonometric function is Here, the angle of the function is sin-1 (x).

Concept explainers

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

Topic Video

Question

### Identifying True Statements in a Scalene Triangle

Consider the right-angled triangle $ \Delta CAB $ shown in the diagram. For this triangle:

- $ \angle CAB $ is represented by $ \alpha $
- $ \angle CBA $ (the right angle)
- $ \angle ADB $ is represented by $ \beta $

The triangle has sides labeled as follows:
- Side $ a $ opposite angle $ \alpha $
- Side $ b $ adjacent to angle $ \alpha $
- Hypotenuse $ c $

### Problem Statement

Identify ALL of the following statements that are true in the given $ \Delta CAB $ where $ \alpha + \beta = 90^\circ $: (1 point)

- **A.** $ \sin(\beta) = \cos(\alpha) $
- **B.** $ \tan(\beta) = \tan(\alpha) $
- **C.** $ \cos(\beta) = \sin(\alpha) $
- **D.** $ \cos(\beta) = \sin(90^\circ - \alpha) $

**Answer Options:**

- ☐ A
- ☐ B
- ☐ C
- ☐ D

### Diagram Explanation

The diagram provided is a right-angled triangle labeled $ \Delta CAB $:

- $ \angle CBA = 90^\circ $
- $ \angle CAB = \alpha $
- $ \angle ADB = \beta $
- Side opposite $ \alpha $ is $ a $
- Side adjacent to $ \alpha $ is $ b $
- Hypotenuse is $ c $

### Analysis of Statements

- **Statement A:** $ \sin(\beta) = \cos(\alpha) $
- By trigonometric identity in a right triangle, this is true because $ \beta = 90^\circ - \alpha $. Therefore, $ \sin(\beta) = \sin(90^\circ - \alpha) = \cos(\alpha) $.

- **Statement B:** $ \tan(\beta) = \tan(\alpha) $
- This is false. $ \tan(\beta) = \tan(90^\circ - \alpha) = \cot(\alpha) $. Therefore, \( \tan(\beta) \neq \tan(\alpha)

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

$Fundamentals of Trigonometric Identities$

Learn more about

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