Solve the triangle:

Question

Solve the triangle: α = 40°, a = 15, b = 13.

a) β = 47.9°, γ = 92.1°, c = 23.7

b)No solution

c)β = 47.9°, γ = 92.1°, c = 20.2

d)β = 33.9°, γ = 106.1°, c = 22.4

Answer 1

Triangle ABC, A on the left, B on top, C on the right

a=15, b=13, a=40

law of sines says:

sin A/ a = sin B/ b

sin 40/15 = sin B/ 13

(13/15)*sin 40 = sin B

B = inverse_sine ( (13/15)*sin 40 )

= 33.85 degrees approximately

This forces angle C = 180 - 40 - 33.85 = 106.14572...

Law of says again says:

sin 40/15 = sin 106.14572/ c

c = 15 * sin 106.14572/ sin 40 = 22.415

option D

Answer 2

For this problem, you will be using the Law of Sines, which is as follows:

sinA/a = sinB /b = sinC/c

where A, B, and C refer to angles of a triangle and a, b, and c refer to sides of a triangle.

1.) Find the angle of b using the Law of Sines:

sin40°/15 = sinB/13

sinB = (0.643/15)13 = (0.043)13 = 0.557

B = sin^-1(0.557) = 33.9°

2.) To find the third angle, we will use the fact that all the inside angles of a triangle equals 180°.

180° = 40 + 33.9° + C

C = 106.1°

3.) We will again use the Law of Sines to find the length of side c.

sin40°/15 = sin106.1°/c

c = sin106.1°/(sin40°/15) = 0.961/0.0428 = 22.4

Given this information, the correct answer is D.