If angles A, B, C of a Triangle ABC from an increasing Ao, then sin B =
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We are given that the angles A, B, and C of a triangle △ABC form an increasing arithmetic progression (AP). We need to find the value of sin B.
Step 1: Properties of angles in a triangle
The sum of the angles in any triangle is:
A + B + C = 180°.
Since A, B, and C form an increasing arithmetic progression, let the common difference of the AP be d. Then we can write:
A = B – d, B = B, C = B + d.
Substitute these into the angle sum property:
(B – d) + B + (B + d) = 180°.
Simplify:
3B = 180°.
Solve for B:
B = 60°.
Step 2: Find sin B
Now that we know B = 60°, we use the standard trigonometric value:
sin 60° = √3/2.
Step 3: Final Answer
The value of sin B is:
√3/2.
The correct answer is:
b) √3/2
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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https://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/