Home Forums Hunting & Shooting Hunter's Campfire More Caveman math...

Had to take a break. Momma sat a plate of bacon, eggs, and a toasted English muffin in front of me. Then I had to get the HP 35 S from the desk drawer.

25/ 3= 8.33 sq root is 2.88 equals height of triangle.

2x25/3 = 16.66 sq root is 4.08 equals base of triangle

check the math:
4.08 sq = 16.64
2.88 sq = 8.29
8.29 + 16.44 = 24.73 because I only carried two decimal places.

It can not be a true 3-4-5 triangle and maintain the 2/1 ratio of base to height.

Correct.

Never said it was...

Us Cavemen only use 3-4-5 triangles when laying out our cave entrances... or doing Caveman Woolly Mammoth cave art...

Why is our math different?

ETA: at 24.98 for hyp square, yours is obviously more acccurate.

No you did not. But some seemed to be working under that assumption.

Ain't math fun...

It’s not a 3,4,5 right triangle. It’s a 30, 60 right triangle where, if the short side is 1, the hypotenuse is 2 and the longer side is 1.732. So the hypotenuse is double the short side. The other, longer side is 1.732 times the short side, 1.732 being the square root of 3.

Why did you sort out the angles?

And are you sure it is a 30-60-90?

I most certainly did not miss it! It is your undoing! When you state that the two double ticked portions of BC (shown below in a later image) are each 2.5, then BC as well as AB and CD are 5. They cannot then also be 4.33.

Note that none of AB, BC, or CD is the hypotenuse. As determined by my and N8r's point E, AE and DE are.

Except the drawing specifically shows the base as twice the height, with the hypotenuse as 5.

If the base is twice the height, the hypotenuse must be longer than that.

FYI...

And Ya done made me pull out my Caveman calculator for the angles...

Geez.

Pythagoras states that a^2 + b^2 = c^2. The problem further constrains b:a be 2:1. CK and N8r mistakenly impose c:a to be 2:1 as a condition. It is not. There is no 30-60-90 triangle.

If you want to specify the short side as the base, the hypotenuse is double the base and the vertical side is 1.732 times the base.
Just do a quick search for 30, 60 right triangle.

In this drawing AB = CD <> BC! Look at it! 4.33 = 4.33 <> 5!

I yield... You are correct.

BC is indeed 4.33... NOT 5.

The 2.5 shown above should be 2.17

The angles are 25.7, 64.3 and 90.

Look at the drawing again. It is specifically NOT a 30-60-90 triangle.

The hypotenuse is identified as 5.
The base is identified as 2 x height.

The longest side of a right triangle is, by definition, the hypotenuse.
The shortest side is commonly referred to as height.
The base is commonly referred to as the longer leg attached to the right triangle.

Here, the base is 2 X height. Hypotenuse sq equals base sq plus height sq.

25 equals base sq plus height sq.

NO!!! 2.17, 4.33, 5 violates Pythagoras for a right triangle. Sqrt(5), Sqrt(20), and 5 make up the triangle. AB is Sqrt(20).

The work:
AE^2 = AB^2 + (AB/2)^2
4*AE^2 = 4*AB^2 + AB^2
4*AE^2 = 5*AB^2
AB^2 = 4/5*AE^2
AB^2 = 4/5*5^2
AB^2 = 20
AB = Sqrt(20)

The base of the large rectangle is 10 (a given).
The two sides of the rectangle are 6 (a given)
A line drawn from the highest point of both sides therefore bisects line BC so each half is 2.5. That gives two congruent triangles with two known sides…2.5 and 5.
A right triangle with one aide = 2.5 and the hypotenuse is 5 defines a 30. 60 right triangle.
In a 30, 60 right triangle the longer side is 1.732 times as long as the shorter side.
1.732 X 2.5 = 4.33.

By definition , the hypotenuse is the side opposite the right angle. If the hypotenuse is 5 and one of the sides adjacent to the right angle is 2.5, the other side adjacent to the right angle is 1.732 times the short side (1.732 is the square root of 3).
So A (2.5) squared plus B (4.33)squared does indeed = C (5) squared or 25

In my math, I assumed the square of base would be a 2/1 ratio with sq of height. Obviously not true.