MATH SOLVE

4 months ago

Q:
# Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degreeA = 119°, a=7, b=4Question 7 options:one solution; c ≈ 7; B = 30°; C = 119°no solutionone solution; c ≈ 4; B = 31°; C = 30°one solution; c ≈ 4; B = 30°; C = 31°

Accepted Solution

A:

Answer:The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°. Option D is correct.Step-by-step explanation:if angle A is obtuse and if a > b then the triangle has one solutionWe are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.Finding remaining side c and ∠B and ∠CUsing Law of sines to find ∠Ba/sin A = b/sin B7/sin 119° = 4/sin B7 * sin B = 4 * sin 1197*sin B = 4(0.874)sin B = 3.496/7B = sin^-1(0.4994)B = 29.96 = 30°We know that sum of angles of triangle = 180°So, 180° = 119° + 30° +∠C180° = 149° + ∠C=> ∠C = 180° - 149°∠C = 31°Now finding cb/sin B = c /sin C4/Sin 30 = c/sin 314* sin 31 = c*sin 304*0.515 = c* 0.5=> c = 4*0.515/0.5c = 4.12 ≈ 4So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.