Question
Download Solution PDFIn a triangle ABC, ∠A = 75° and ∠B = 45°. What is 2a - b equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFTriangle Angle Sum Property:
- In a triangle, the sum of all interior angles is always equal to 180º.
- Given angles can be used to find the unknown angle using the formula:
- Once all angles are known, trigonometric ratios can be used to relate the sides of the triangle.
- Law of Sines:
- The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:
- Here, a, b, and c are the sides opposite to angles A, B, and C respectively.
Calculation:
Given,
Angle A = 75º
Angle B = 45º
Using the triangle angle sum property, find angle C:
⇒ ∠C = 180º - (∠A + ∠B)
⇒ ∠C = 180º - (75º + 45º)
⇒ ∠C = 180º - 120º
⇒ ∠C = 60º
Now, using the Law of Sines:
⇒
⇒
Now
⇒ 2a - b =
∴ Option (b) is correct.
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