Triangle ABC has C as the right angle. Fang recalls that the value of sin A has a numerator of 15. Manga remembered that the value of sin A is less than the value of cos A. What is the value of cos A?
The problem has originally been published at https://stemgeeks.net/@savvyplayer/mayday3math.
√(2)/2 < cos A < 1 🎯
Answers which say that there is not enough information in the given will also be considered correct. 😁
Based on the given on the original problem, we have the following facts:
- C is the right angle
- sin A = 15 / BC
- sin A < cos A
Based on the facts above, we can derive the following:
- A and B are acute angles
- AC > BC, so AC > 15
- AB > 15√2 using Pythagorean theorem
- cos A = AC/AB, so cos A > √2/2
- Both AC and AB has an upper bound of positive infinity, which will approach 1, so cos A < 1
Using the last two derived facts above, we get
√2/2 < cos A < 1.
Winner: @minus-pi 🏅
1 HIVE has been sent to @minus-pi's Hive account. 💰
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