The solution of right triangles

In plane geometry it is shown that if two sides and one acute angle of a right triangle are given, the triangle can be constructed and the unknown sides and angles found by meas­urement. The same result can be obtained much more accu­rately by means of the modified definitions of the trigonomet­ric functions. Each of these expressions involves three parts of the triangle. By selecting an expression involving the two known parts and an unknown part which is to be found, an equation is obtained which can be solved for the unknown part.

Briefly, the following rules can be used to solve the un­known part of a right triangle:

1.To find the acute angleα, knowing the acute angle β, use the formula: α=90°—β

2. To find an unknown acute angle, knowing two sides but not the other acute angle, select the proper relation involv­ing the unknown angle and the two known sides.

3. To find an unknown side, knowing one side and one acute angle from the relations below select the one most easily used.

Unknown side = Hypotenuse • Sine of = Hypotenuse • Cos of angle

angle opposite adjacent to unknown side

unknown side

Unknown side = Known side • Tangent of = Known side-Cotangent of

Angle opposite unknown side angle adjacent to unknown side

Hypotenuse = Known side • Sine of = Known side • Cosine of angle adjacent

Angle opposite known side to known side