Question about 30:60:90 (noob)

  • Thread starter HenryKhais
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In summary, the conversation is about watching a Khan Academy video on using the Pythagorean theorem to solve for the height of a 30-60-90 triangle. The formula for the Pythagorean theorem is discussed, and at the 8 minute mark in the video, there is confusion about adding '4' as the denominator under h^2 and how A was derived. The response suggests breaking down the equation and shows that 1/4*h^2 is equivalent to h^2/4. The person asking the question is self-teaching and seeking a better understanding of the concept.
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HenryKhais
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Im watching one of khan's videos:
http://www.youtube.com/watch?v=Qwet4cIpnCM&feature=player_embedded#at=468

And he's using the pythagorean theorem to solve height of a 30-60-90 triangle.
Prior to everything, I think I have a good understanding on how it all works, however, I still don't feel like I understand it fully.

From what I understand, pythagorean theorem's formula is: base^(2) x height^(2) = hypotenuse^(2).

Now if you watch the video and skip to the 8:00 mark, everything seems to make sense to me except the part where he adds '4' as the denominator under h^(2), nor do I understand how he got 'A=h^(2)(1 - 1/4).
Where did the 4 come from?

Sorry if this is an obvious question, I am self teaching and really just want to learn and fully understand it.

Thanks =)
 
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  • #2
From the video at the 8 min mark,

[1/2*h]^2 = [1/2]^2*[h]^2 = 1/4*h^2 = h^2/4

Does this help?
 

1. What is the concept of 30:60:90 in science?

The concept of 30:60:90 in science refers to the angles of a right triangle. It is often used in geometry and trigonometry to represent the ratio of the sides of a right triangle.

2. How do you find the sides of a 30:60:90 triangle?

To find the sides of a 30:60:90 triangle, you can use the Pythagorean theorem. For a 30:60:90 triangle, the shorter leg is half the length of the hypotenuse, and the longer leg is √3 times the length of the shorter leg.

3. What is the significance of a 30:60:90 triangle?

A 30:60:90 triangle is significant because it is a special right triangle with specific angles and ratios that are commonly used in mathematics and physics. Its properties make it easier to calculate and measure certain values in real-life situations.

4. Can you give an example of a 30:60:90 triangle in real life?

One example of a 30:60:90 triangle in real life is a roof of a house. The slope of the roof forms a 30 degree angle with the ground, the pitch of the roof forms a 60 degree angle with the ground, and the length of the roof forms the hypotenuse of the triangle.

5. How is 30:60:90 used in science and engineering?

The 30:60:90 triangle is used in science and engineering to calculate and measure various quantities, such as forces, distances, and angles. It is also used in constructing and designing structures, circuits, and other systems.

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