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Answer :
Answer:
b= 23.4,. γ = 70°, c= 28.9
Step-by-step explanation:
To solve the triangle with given α = 65°, β = 45°, and a = 30, we can use the law of sines:
b/sin(β) = a/sin(α)
b/sin(45°) = 30/sin(65°)
b ≈ 23.4
Then, to find angle γ, we can use the fact that the sum of angles in a triangle is 180°:
γ = 180° - α - β
γ ≈ 70°
To find side c, we can again use the law of sines:
c/sin(γ) = a/sin(α)
c/sin(70°) = 30/sin(65°)
c ≈ 28.9
Therefore, the solution is b = 23.4, γ = 70°, and c = 28.9.
Note that there is no other possible solution, as the given angles and side lengths do not allow for multiple triangles to be formed.
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