Repeat the steps above for the similar triangle built on the other side of the original triangle.Įventually, we apply the property of parallel lines and identify the last right triangle with the acute angle ( θ + φ \theta+\varphi θ + φ). Call the corresponding angle θ \theta θ, and calculate the sides: hint: it suffices to multiply the sine and cosine of θ \theta θ by the hypotenuse ( cos ( φ ) \cos(\varphi) cos ( φ )). Now add another right triangle below the original one, with the hypotenuse equal to the side cos ( φ ) \cos(\varphi) cos ( φ ) of the original triangle. Using the relationship between right triangles and trigonometric function, you can easily find the length of the sides ( sin ( φ ) \sin(\varphi) sin ( φ ) and cos ( φ ) \cos(\varphi) cos ( φ )).
Start by tracing a right triangle with hypotenuse 1 1 1, and call one of the angles φ \varphi φ.
