In the figure, the height of △ ABC is h m. AB= 100, angle A =40° and angle B= 30°
. Find the value of h , correct to 1 decimal place
Math summer assignment
2014-08-08 4:37 am
回答 (3)
2014-08-08 8:50 am
✔ 最佳答案
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.
參考: pingshek, pinghshek
2014-08-08 9:14 am
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
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
2014-08-08 5:24 am
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。
h/x = tan40⁰ = 0.8391
h/(100-x) = tan30⁰ = 0.5774
解解看。
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