Question

Solve the triangle. a=20,b=25,c=15 A≈ (Round to one decimal place as needed.) B≈ ∘ (Round to one decimal place as needed.) C≈ (Round to one decimal place as needed.)

Answer 1

To solve the triangle with side lengths a = 20, b = 25, and c = 15, we can use the Law of Cosines and the Law of Sines. Using the Law of Cosines, we can find angle C to be approximately 137.4 degrees. Then, using the Law of Sines, we can find angles A and B to be approximately 30.7 degrees and 11.9 degrees, respectively.

Step-by-step explanation:

To solve the triangle with side lengths a = 20, b = 25, and c = 15, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds: c^2 = a^2 + b^2 - 2ab*cos(C).

Substituting the given values, we have 15^2 = 20^2 + 25^2 - 2*20*25*cos(C). Simplifying this equation gives cos(C) = -27.5/25. Solving for C, we find that C ≈ 137.4 degrees.

To find the remaining angles A and B, we can use the Law of Sines. The Law of Sines states that in a triangle with sides a, b, and c, and opposite angles A, B, and C respectively, the following equation holds: sin(A)/a = sin(B)/b = sin(C)/c.

Substituting the known values, we have sin(A)/20 = sin(B)/25 = sin(137.4)/15. Solving for A and B using trigonometric identities, we find that A ≈ 30.7 degrees and B ≈ 11.9 degrees.

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