Question

Solve the triangle? when A = 24.3 B = 14.7 C = 18.7

Answer 1

Vertices:

`A = arccos( -353/7854)`

`B = arccos( 72409/90882)`

`C = arccos(6527/10206)`

Explanation:

Hey people, let's use lower case letters for triangle sides and upper case for the vertices.

These are presumably sides: `a=24.3, b=14.7, c=18.7`. We're after the angles.

Pro Tip: It's generally better to use cosine than sine in a number of places in trig. One reason is that a cosine uniquely determines a triangle angle `(`between `0^circ` and `180^circ),` but the sine is ambiguous; supplementary angles have the same sine. When you have a choice between the Law of Sines and the Law of Cosines, choose cosines.

`c^2 = a^2 + b^2 - 2 a b cos C`

`cos C = {a^2 + b^2 - c^2}/{2 a b}`

`cos C = {24.3^2 + 14.7^2 - 18.7^2}/{2 (24.3)(14.7)} = 6527/10206`

`cos A = { 14.7^2 + 18.7^2 - 24.3^2 }/{2( 14.7)(18.7)} = -353/7854`

Negative, an obtuse angle, but small, just a bit more than `90^circ`.

`cos B = { 24.3^2 + 18.7^2 - 14.7^2 }/{2( 24.3)(18.7)} = 72409/90882`

I hate ruining an exact answer with approximations, so I'll leave the inverse cosine calculator work to you.