In triangle ABC, A=115degrees, a=65 m, b =32m. Solve the triangle completely.​

Here is an example, and you can plug your own numbers into the equations and solve.

law of sines is:

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

you have:

a = 70m

b = 31m

A = 115 degrees.

the part of the law can use is:

a/sin(A) = b/sin(B)

this equation becomes:

70/sin(115) = 31/sin(B)

multiply both sides of this equation by sin(115) and multiply both sides of this equation by sin(B) and you get:

70 * sin(B) = 31 * sin(115)

this is the same thing you would do if i told you to cross multiply.

now divide both sides of the equation by 70 to get:

sin(B) = (31 * sin(115) / 70

use your calculator to solve for sin(B) to get:

sin(B) = (31 * .906307787) / 70 which becomes:

sin(B) = 28.0955414 / 70 which becomes:

sin(B) = .401364877

use your calculator to solve for B to get:

B = arc sin(.401364877) = 23.6635313 degrees.

confirm by plugging into your original equation to get:

a/sin(A) = b/sin(B) becomes:

31/.401364877 = 70/.906307787 which becomes:

77.23645433 = 77.23645433, confirming the answer for angle B is good.

your answer is:

A = 23.6635313 degrees

you now have:

a = 70m

b = 31m

A = 115 degrees.

B = 23.6635313 degrees.

C = 180 - A - B = 41.3364687

this is because the sum of the angles of a triangle must be equal to 180 degrees.

you can use the law of sines again to solve for c.

you can use either:

a/sin(A) = c/sin(C)

or you can use:

b/sin(B) = c/sin(C)

either one will get you the answer.

using b/sin(B) = c/sin(C), we get:

31/sin(23.6635313) = c/sin(41.3364687), we get:

c = (31 * sin(41.3364687))/sin(23.6635313) which gets:

c = 51.0131112

you now have:

a = 70m

b = 31m

c = 51.0131112

A = 115 degrees.

B = 23.6635313 degrees.

C = 41.3364687

confirm the answer is correct by taking any angle and deriving the common ratio.

take a/sin(A) to derive k = 77.23645433

if all is good, then:

b/k = sin(B) which makes B = 23.6635313

c/k = sin(C) which makes C = 41.3364687

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