math problem
2008-08-17 5:43 pm
A 50-foot wire runs from the roof of a building to the top of a 10-foot pole 14 feet across the street. How much taller would the pole have to be if the street were 16 feet wider and the wire remained the same length?
回答 (1)
2008-08-18 5:02 am
✔ 最佳答案
Let the building is taller than the 10ft pole by x ft. Then by Pythagoras theorem, x^2 + 14^2 = 50^2
x^2 = 50^2 - 14^2 = (50+14)(50-14) = (64)(36)
x = (8)(6) = 48ft.
Therefore, the building is 48 + 10 = 58ft tall.
Now the street is 16ft wide. Let the pole be y ft tall. Again by Pythagoras theorem,
(58 - y)^2 + 16^2 = 50^2
(58 - y)^2 = 50^2 - 16^2 = (66)(34) = 2244
58 - y = sqrt(2244)
y = 58 - sqrt(2244) = 10.63 ft.
therefore, the pole should be taller by 10.63 - 10 = 0.63 ft.
收錄日期: 2021-04-25 22:37:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080817000051KK00551