Result of the Day 3 Challenge of my May 2021 Math trigonometry mini-contest for D.Buzz 😎

in STEMGeeks β€’ 2 months ago

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

triangle.png

Sorry for the gritty graphics, because I used MS Paint to draw the image above! πŸ˜…

Β 
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 πŸ…

1 HIVE has been sent to @minus-pi's Hive account. πŸ’°

Mentions: @jfang003, @holovision, @ahmadmanga (@ahmadmangazap), and @eturnerx (@eturnerx-dbuzz) πŸ€“
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🀯

Posted with STEMGeeks