# Day 4 Problem

## Vision knew that the value of tan (2A), where A is one of the acute angles of a right triangle with integer sides, has a value of approximately 1.0084. What is the minimum possible area of the triangle?

*This problem was originally published at https://stemgeeks.net/@savvyplayer/mayday4math*.

# Answer

## 30 square units 🎯

# Solution

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

The given says the following facts:

- tan (2A) ≈ 1.0084
- A is an acute angle
- The triangle has integer sides

Based on the facts above, we can derive the following:

- A ≈ arctan (1.0084) / 2 ≈ 22.6198
- tan (A) ≈ tan (22.6198) ≈ 0.4167
- using geometric series to attempt to convert 0.4167 to fraction, we get 4167/9999 ≈ 5/12
- tan (A) ≈ 5/12

Based on the last derived fact above, the opposite side of the angle is 5 units, and the adjacent side measures 12 units. Since we have the measures of both the *legs* of the right triangle, we can now use the formula for the area of the triangle, which will give us an area of **30 square units**.

# Winner: *none* 🤯

Today's prize of 1 HIVE has been ~~split depending on the number of winners in the previous days for this month's contest and~~ sent to the only winning participant so far for this month's Math mini-contest for D.Buzz, which is no other than @minus-pi! 💰😅

- @minus-pi forgot to add the "square units" on his answer! 🤯 Regardless, he has still received the full prize of 1 HIVE for today because nobody has tried to compete with him so far! 😅

Mentions: @jfang003, @holovision, @ahmadmanga (@ahmadmangazap), and @eturnerx (@eturnerx-dbuzz) 🤓

Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯

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