Math summer assignment

The answer is as follows :


圖片參考：https://s.yimg.com/lo/api/res/1.2/AKJbGs9WVk54VRY3lUA_Bw--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/https://farm4.staticflickr.com/3915/14850486534_8d1758c188_o.png


https://farm4.staticflickr.com/3915/14850486534_8d1758c188_o.png

2014-08-08 00:51:26 補充：
Amendment :
In the diagram, the height should be h m or h instead of h cm.

Suppose the height is perpendicular to AB.

By sine law,
AB/sin(180⁰-40⁰-30⁰)=AC/sin(30⁰)
AC=50 / sin 110⁰
Area of triangle ABC=(1/2) AB AC sin 40⁰=(1/2) 100*(50 / sin 110⁰) sin 40⁰
Another method to calculate the area=100h/2

100h/2=(1/2) 100*(50 / sin 110⁰) sin 40⁰
h=50 sin 40⁰ / sin 110⁰

設 D 為 h 在 AB 上的 垂足。AD = x; DB = 100-x

h/x = tan40⁰ = 0.8391

h/(100-x) = tan30⁰ = 0.5774

解解看。