### 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)- \( \angle ADB \)