Question

Solve the triangle: α = 40°, β = 35°, and a = 10.

Answer 1

The triangle: α = 40°, β = 35°, and a = 10. is b = 8.9, γ = 105°, c = 15.0

What is Sine Law?

If A, B, and C are the measurements of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite of the corresponding angles, then the ratios of the a side’s length to the sine of the angle opposite the side must all be the same.

a/ sin A = b/ sin B = c/ sin C

Using Angle sum property in a triangle we have,

α+β+ γ = 180

40+35+ γ=180

γ= 180-75

γ= 105°

Now,

c/ sin γ= a/ sin α

c/ sin 105= 10/ sin 40

c/ 0.96592 = 10 /0.6427

c = 15

again,

b/ sin  β=  a/ sin α

b/ sin 35=  10/ sin 40

b/0.5737= 15.559

b= 8.92

Learn more about sine law here:

brainly.com/question/17289163

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