RE: Math mini-contest problem for Day 7 on D.Buzz 😎

Answer for Day 7 Math Problem

3.22 meters 🎯

It does not matter if any of Manga, Fang, or Vision is standing on higher or lower ground, because their distances and angles shall stay the same; there will always be a way to draw a triangle on 3-dimensional space whose vertices are the positions of the 3 people in the given.

Solution

The problem is in trigonometry.

Manga, Fang, and Vision form a logical triangle.

Let M = Manga's position
Let F = Fang's position
Let V = Vision's position

The triangle is FVM.

side MF = 5.75 meters
side MV = 5.75 meters
angle FMV = 32.5°

The given are two sides and an included angle, so the best formula to use is the Law of Cosines.

The Law of Cosines is the following:

c^2 = a^2 + b^2 - 2 * a * b * cos ACB

... where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite the sides with the same letter.

c^2 = (5.75)^2 + (5.75)^2 - 2 * (5.75) * (5.75) * cos (32.5°)
c^2 = 10.3557
c = 3.2180

Fang and Vision are 3.22 meters from each other.

Winner: @dkmathstats 🏅

1 HIVE has been sent to @dkmathstats's Hive account. 💰

I am aware that @dkmathstats's answer was slightly off by at most 0.005 meters, which was probably because of rounding error. Nevertheless, his answer was very close to the correct answer, so I accepted it.

Mentions: @jfang003, @holovision, and @ahmadmanga (@ahmadmangazap)
Special mentions: @chrisrice, @jancharlest

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