Discovering the Truth Behind the Side Ratios of a 30:40:90 Triangle

In summary, Godfree asks if it is true that the side ratio for a 30:40:90 degree right triangle is 1 : √3 : 2. He also wonders if this ratio can be multiplied by certain numbers to obtain the Pythagorean identity, but not by 4. In response, Cap'n points out an error in the original statement and agrees with Epicurius' sentiments about religion and science.
  • #1
DeusAbscondus
176
0
(Plse bear with me: until i learn how to fly this thing, / must stand for radical)

If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2
then, is the following true:

one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4

If so, why not?

Thx,
Godfree
 
Mathematics news on Phys.org
  • #2
DeusAbscondus said:
(Plse bear with me: until i learn how to fly this thing, / must stand for radical)

If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2
then, is the following true:

one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4

If so, why not?

Thx,
Godfree

A right triangle cannot have 30 and 40 degrees for its other two angles, in fact if the side rations of a triangle are \(1,\ \sqrt{3},\ 2\) then it is a 30,60,90 degree triangle

CB
 
  • #3
Thank's Cap'n; it was an arithmetic error, that was all...
I'll be more careful before posting next time... sheeesh, i wasted 4 hours looking at this today, and kept making the same tiny error in my math...
Anyway, i heartily concur with Epicurius' sentiments and, by inference, your core values: i find a lot in common with non-believers, with atheists actually (why be coy) but I'm constantly amazed at how people (like my teacher) can do higher maths and still believe in invisible friends in the sky, and hold a young Earth model in the same brain. Enough off-topic.
Thanks again,
 

FAQ: Discovering the Truth Behind the Side Ratios of a 30:40:90 Triangle

What is the triangle ratio question?

The triangle ratio question refers to a type of mathematical problem that involves finding the ratio of the sides of a triangle. This ratio is often used to determine the relationship between the different sides of a triangle and can be used to solve various geometry problems.

How do you solve a triangle ratio question?

To solve a triangle ratio question, you can use the Pythagorean theorem or trigonometric ratios such as sine, cosine, and tangent. First, identify which sides of the triangle are given and which are unknown. Then, use the appropriate formula to find the missing side or angle.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental formula in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It can be written as a^2 + b^2 = c^2, where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

How do you use trigonometric ratios to solve a triangle ratio question?

Trigonometric ratios, such as sine, cosine, and tangent, can be used to solve a triangle ratio question by relating the angles of a triangle to the lengths of its sides. For example, in a right triangle, the sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse.

Why are triangle ratio questions important?

Triangle ratio questions are important because they help us understand the relationship between the different sides and angles of a triangle. This information is useful in various fields such as engineering, architecture, and physics, where triangles are commonly used to represent and solve real-world problems.

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