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Find 20 Pythagorean theorem to solve more problems!
Xiao Ming put a triangular plate together as shown in the figure. He found that as long as the length of one side is known, the length of other sides can be calculated. If CD = 2 is known, the length of AC can be obtained
Please help us to solve a proof problem using the knowledge of Pythagorean theorem Let a, B, C, d all be positive numbers. You can prove with Pythagorean theorem that the root sign a ^ 2 + C ^ 2 + D ^ 2 + 2CD + the root sign b ^ 2 + C ^ 2 > the root sign a ^ 2 + B ^ 2 + D ^ 2 + 2Ab
Now we simplify the first root sign, then take a and C + D as right angle sides, the second root sign takes B and C as right angle sides, and the third root sign takes a + B and D as right angle sides to draw three triangles. Pay attention to the position, first draw the first, and then draw the second with C + D as the common edge. In this way, C and D on C + D are clear. Note that a and B do not draw on a straight line, and then translate B, Translation to and a on a straight line, so as to construct a + B, and then flip the oblique line of the second right triangle, so as to form a new triangle with the hypotenuse of three triangles. In this triangle, the conclusion is drawn by using the sum of two sides and greater than the third side,
A problem about Pythagorean theorem A 701cm long wooden stick should be placed in a cuboid wooden box with the length, width and height of 50cm, 40cm and 30cm respectively. Can it be put in? (hint: the height of the cuboid is perpendicular to any straight line on the bottom.) It's 70cm, not 701cm
(let the box base on the plane of height and width)
The length of the diagonal on the bottom of the cuboid = root (30 square + 40 square) = 50
Because the length of 50cm is perpendicular to the diagonal (because the diagonal is inside the bottom)
Therefore, the length of the longest line segment in the cuboid is 50 root sign 2 ≈ 70.7
In other words, you missed a decimal point
If the length is 70.1, it can be put in
Several Pythagorean theorem problems in the second year of junior high school, 1. If the perimeter of a right triangle is 2 + radical 6, and the length of the hypotenuse is 2, then the area of the right triangle is? This is a treasure map of someone on the island. After landing, he walked 8 kilometers east and 2 kilometers north. After encountering obstacles, he went west for 3 kilometers, then went north for 6 kilometers, and turned East for only one kilometer to find the treasure. What's the straight-line distance from the landing point to the treasure spot? (you can draw a picture, I can't do the above picture, sorry.)
One
Length + width of right triangle = 2 + √ 6-2 = √ 6
If the length is x, then the width is √ 6-x
Pythagorean theorem: x2 + (√ 6-x) 2 = 4
X2-（√6）X+1=0
X=（√6+√2）/2
X′=（√6-√2）/2
The area of a right triangle is:
1/2【（√6+√2）/2】×【（√6-√2）/2】
=1/8×（√6+√2）×（√6-√2）
=1/8×（6-2）=1/2
Two
This man is heading East: 8-3 + 1 = 6 km
The man went north: 2 + 6 = 8 km
The two right sides of a right triangle are: 6 and 8
Straight line distance from landing point to treasure point (bevel side)
Square = 100 square + 6
(hypotenuse) = 10 km
Use Pythagorean to understand a problem, thank you The cross section of a tunnel is a semicircle with a radius of 3.6 meters. Can a truck with a height of 2.4 meters and a width of 3 meters pass through the tunnel? Check on the Internet, there is the answer to this question, but did not say why, just solve it like this Always can't understand, ha ha, you clear and easy to understand to help me to answer, thank you
If the car goes from the middle of the tunnel, the wheel span is 1.5 meters around the center of the circle. The height from the side wall of the car to the tunnel is h. at this time, the span is 1.5, the height h and the tunnel radius form a right triangle. H ^ 2 + 1.5 ^ 2 = 3.6 ^ 2, H = 3.27 m, the height of the car itself is only 2.4 m, so it will not meet
There is a problem of Pythagorean theorem, Given that a, B, C are the three sides of the right triangle ABC, the angle c = 90 degrees, a = 9, B, C are all integers, then the perimeter of this triangle is () a.4a, b.9a, c.10a, d.4a or 10A?
a. B, C, are all integers, Pythagorean numbers
Then, the number of shares that meet the conditions is
3. 4,5 and 9,40,41
3. The combination of 4 and 5 needs to be calculated
a=3*3=9
b=4*3=12
c=5*3=15
a+b+c=36
Answer D
Send you 100 or less of the number of shares for future use
a b c
3 4 5
5 12 13
7 24 25
8 15 17
9 40 41
11 60 61
12 35 37
13 84 85
16 63 65
20 21 29
28 45 53
33 56 65
36 77 85
39 80 89
48 55 73
65 72 97
Thinking, formula, In a right triangle, the circumference is 60 and the ratio of hypotenuse to right angle side is 13 to 5 The equation is listed: (the number in brackets represents the power) (5x)(2)+(60-5X-13x)(2)=(13x)(2) However, at the current level of grade two, the equation can not be solved. Is there any other idea or algorithm? Or is there a way to solve it?
Let a right angle side be 5a, an oblique side is 13a, then the other right angle side is 12a (Pythagorean theorem) 12a + 13A + 5A = 60 a = 2, so three sides are 102426
The mathematical problems of grade two in junior high school understood by Pythagorean Taking the three sides of a right triangle as the side length, three positive n-sided forms are made. Do their areas meet the requirement that the sum of the two small ones equals the large one, that is, S1 + S2 = S3? Yes or no Whether or not, take an equilateral triangle as an example Wait till I show it to the teacher tomorrow
yes
Suppose that the three sides of a right triangle are a, B, C, and a? + B? = C
The areas of the three equilateral triangles are 0.25 √ 3 A ^, 0.25 √ 3 A ^, and 0.25 √ 3 C? Respectively (space means multiplication) (reason: if a regular triangle is made of a height, each side is a, and the height of Pythagorean is 0.5 √ 3 A, then the area is 0.25 √ 3 a 2)
So the sum of the areas of the triangles made with two right angles is 0.25 √ 3 a? 2 + 0.25 √ 3 a? = 0.25 √ 3 (a? + B?)
The sum of the areas of the triangles in terms of hypotenuse is 0.25 √ 3 C 2
Because a? 2 + B? 2 = C
Therefore, 0.25 √ 3 (a? 2 + B? 2) = 0.25 √ 3 C
So yes
(I've talked too much about my girlfriend...)
What is the meaning of line integral in calculus Can you talk about the application of line integral in calculus in physics? And what is line integral in detail!
There are two kinds of line integrals: the first type of curvilinear integral and the second type of curvilinear integral
The first type can be understood as the mass of an object with one-dimensional inhomogeneous density
The second type is the integral of a vector along the tangent direction of the curve
The significance of the first and second type line integral and area integral
The first type of curvilinear integral is related to the arc length. Each arc length differential element DS has a corresponding f (x), which is equivalent to the linear density. After the integration, it is equivalent to the mass of the total length
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