Problem

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.

Answer

√(2)/2 < cos A < 1 🎯

Answers which say that there is not enough information in the given will also be considered correct. 😁

Solution

Sorry for the gritty graphics, because I used MS Paint to draw the image above! 😅
 
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. 💰

Mentions: @jfang003, @holovision, @ahmadmanga (@ahmadmangazap), and @eturnerx (@eturnerx-dbuzz) 🤓
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯

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