Triangle angle math problem

圖片參考：https://sites.google.com/site/emathqss/qs/Fullscreencapture29122011153715.jpg



Let x be the height (as the base is the longest side) , then

x / 5 = sin 30°
x / 5 = 1 / 2
x = 5 / 2

;
x / 3 = sin θ
(5/2) / 3 = sin θ
sin θ = 5 / 6
θ = 56.4° or 123.6°(rejected since θ is a acute angle)


Method 2 :

By sine formula ,

sinθ / 5 = sin30° / 3

sinθ = 5 * 1/2 / 3

θ = 56.4° or 123.6°(rejected since θ is a acute angle)


2011-12-29 16:51:23 補充：
θ = 56° (nearest degree)