Consider a triangle ABC like the one below. Suppose that C=83°, a = 43, and b = 44. Solve the triangle. Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

Explanation:

   In a triangle

a / sin A = b / sinB = c / sinC

Putting the values

43 / sin A = 44 / sinB

sinA / sinB = 43 / 44 = 1 / 1.023

A + B = 180 - 83 = 97

sinA / sin ( 97 - A ) = 1 / 1.023

sin 97 cos A - cos 97 sin A = 1.023 sin A

= .9925 cos A + .122 sin A = 1.023 sin A

.9925 cos A = .901 sin A

squaring

.985 cos²A = .8118 sin²A

.985 - .985 sin²A = .8118 sin²A

.985 = 1.7968 sin²A

sinA = .74

A = 47.73

B = 49.27

c / sin C = b / sin B

c = b sinC / sinB

= 44 x sin 83 / sin 49.27

= 44 x .9925 / .7578

= 57.62

odds are decent that your handwriting right now looks a little bit different than it did five years ago, and will look different again in five more. when i look back through my notebooks from middle school to now, i see a long, slow progression from meticulous and teeny letters to bigger, sloppier ones, plus a few side detours: sometime in high school, for example, i decided those loopy cursive lowercase f’s were just the coolest, adopting them as the lone rep for cursive in my otherwise all-print handwriting.

explanation: