Question

Solve the triangle: α = 65°, β = 45°, and a = 30.

b = 23.4, γ = 70°, c = 28.9
b = 38.5, γ = 70°, c = 28.9
b = 38.5, γ = 70°, c = 31.1
b = 23.4, γ = 70°, c = 31.1

Answer 1

b= 23.4,. γ = 70°, c= 28.9

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.