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How do you calculate the hypotenuse of a right triangle?
The old pythagorean theorem says, "the square of the hypotenuse is equal to the sum of the square of the other two sides." What that means is, get an accurate measurement of the two sides that touch the right angle, square them and add them together then take the square root of that number and you'll have the length of the hypotenuse. In mathematical terms it's: A2+ B2= C2. The hypotenuse of a right angled triangle is the longest side, or the one opposite the right angle. It can be calculated using a variety of methods - Pythagoras theorem : A2 + B2 = C2, where A and B are the sides adjacent to the right angle, and C is the hypotenuse. The square of A plus the square of B is equal to the square of C, so C can be calculated as √(A2 + B2). Trigonometric angle rules : Sin(e) x = o/h, cos(ine) x = a/h, tan(gent) x = o/a, where x is one of the other two angles, o is the side opposite this angle, a is the side adjacent to it, and h is the hypotenuse. Using these angle rules, you can calculate the length of any of the sides given the length of one of the other sides plus an angle. There are others, but they start to become more difficult to explain without other knowledge in triangle geometry! a2+b2=c2 /l / l / l C / l A / l / l / l /____ l B Example: /l / l / l C / l A=4 / l / l / l /___ l B=3 a2+b2=c2 42+32=c2 16+9=c2 25=c2 square root of 25= square root of c2 5=c Answer: /l / l / l C=5 / l A=4 / l / l / l /____ l B=3 Formula: a2+b2=c2 Example: A=4 B=3 C=? a2+b2=c2 42+32=c2 16+9=c2 25=c2 square root of 25= square root of c2 5=c Answer: A=4 B=3 C=5
What is the formula for the determinant of a 3 x 3 matrix?
If the matrix is { a1 b1 c1} {a2 b2 c2} {a3 b3 c3} then the determinant is a1b2c3 + b1c2a3 + c1a2b3 - (c1b2a3 + a1c2b3 + b1a2c3)
What is b square times a square?
b square times a square = b2 x a2 = (ba)2
Why the square of the sum of two numbers is different from the sum of the squares of two numbers?
call the numbers a & b (a+b)2 = a2+2ab+b2 which is greater than a2 + b2 by twice the product of the numbers. Check: say 3 and 5 32 + 52 = 9 + 25 = 34 (3 +5)2 = 64, greater by twice a x b. QED -------------------- If a and b are the numbers, then (a+b)2 = a2 + 2ab + b2, which is different from a2 + b2 (not necessarily larger). The two quantities are equal only when one (or both) of a,b is zero.
Prove that two vectors must have equal magnitude if their sum is perpendicular to their difference?
Suppose the condition stated in this problem holds for the two vectors a and b. If the sum a+b is perpendicular to the difference a-b then the dot product of these two vectors is zero: (a + b) · (a - b) = 0 Use the distributive property of the dot product to expand the left side of this equation. We get: a · a - a · b + b · a - b · b But the dot product of a vector with itself gives the magnitude squared: a · a = a2 x + a2 y + a2 z = a2 (likewise b · b = b2) and the dot product is commutative: a · b = b · a. Using these facts, we then have a2 - a · b + a · b + b2 = 0 , which gives: a2 - b2 = 0 =) a2 = b2 Since the magnitude of a vector must be a positive number, this implies a = b and so vectors a and b have the same magnitude.
If a plus b plus c equals x plus y plus z then prove a2 plus b2 plus c2 equals x2 plus y2 plus z2?
a2+b2+c2=x2+y2+z2 divide each side by 2 (a2+b2+c2)/2=(x2+y2+z2)/2 a+b+c=x+y+z
How do you find the radious of a square?
Use pythagoras theorem a2 + b2 = c2 Solve for c c = sq rt (a2 + b2) radius = 1/2 X c = 1/2 X sq rt (a2 + b2) For a square, a = b = length of one side
What is the diagonal measurement of a 22x22 square?
In a right triangle, a2 + b2 = c2. So, the hypoteneuse, c = (a2 + b2)½. c = (222 + 222)½ = 968½ = (112 x 23)½ = 11 x 2 x 2½ = 22 x 2½ = 22 x 1.4142135623730950488016887242097... = 31.112698372208091073637151932613...
How do you rearrange v squared equals b squared bracket a squared - x squared bracket to make x the subject?
v2 = b2 (a2 - x2)Divide each side by b2 :v2/b2 = a2 - x2Subtract a2 from each side:v2/b2 - a2 = -x2Multiply each side by -1 :x2 = a2 - v2/b2Take the square root of each side:x = ± sqrt ( a2 - v2/b2 )
What is the height of x if the hypotenuse is 21 and the base is 7?
Use the Pythagorean theorem: c2 = a2 + b2, in this example we need to know, let's say a. So that, x2 = c2 - b2 x = √(212 - 72)= √(441 - 49) = √392 = √196*2 = 14√ 2
How do you solve x squared plus 9 equals to zero?
The answer is x = 3i and x = -3i. {Where i= √(-1)}An expression in the form a2 - b2 can be factored into (a - b)(a + b), but you have a2 + b2 so this factors into (a - bi)(a + bi). Check by multiplying the binomials: a2 + abi - abi - (bi)2 the [abi]'s cancel, and i2 = -1, so you have a2 + abi - abi - -b2 which is a2 + b2, so it checks out. In this case, a is x and b is 3.
What is the point of the Pythagorean theorem?
to find if the triangle is right or find missing angles. Ex: a2+b2=c2. Lengths of a triangle are 13, 10 and X. 13 is the hypotenuse so you plug it into the c2 part
What are all the triangle formulas?
Area = (Base x Height) / 2 For a right angle triangle Pythagoreas' Theorem states: a2 + b2 = c2 sum of angles = 180o For a non-right angle triangle: { the Sine Law states: a/Sin(A) = b/Sin(B) = c/Sin(C) for ease of explanation let abc be lengths of a non-right angle triangle. {a / Sin(angle where b meets c)} = {b / Sin(angle where c meets a)} = {c / Sin(angle where a meets b)} The Cosine Law states: (with respect to the above example) a2 = b2 + c2 - 2bc Cos(A) b2 = a2 + c2 - 2ac Cos(B) c2 = a2 + b2 - 2ab Cos(C) }
Why does the Pythagorean theorem work on only right triangles?
There is a Pythagorean theorem that actually works for every triangle. Its just that for right triangles it can be simplified to A2+B2=C2 due to the properties of cosines. The law of cosines states that for a triangle with sides A, B, and C, and angles a, b, and c (with side C being opposite angle c), C2 = A2 + B2 - (2 x A x B x cos c). This formula will work for any triangle. Now imagine that we are talking about a right triangle, with side C the hypotenuse (just like in the classic Pythagorean theorem) and angle c the right angle. The cosine of a 90 degree angle is 0, which means that the part in bold would completely drop out of the equation, leaving us with A2+B2=C2 . The cosine of any other angle possible on a triangle would result in some other number, making A2+B2=C2 not work.
Can you show a b c the whole square?
It's easy to evalute (a + b + c)2..... Let x = (a + b)....then expand (x + c)2 as you would normally in the case of binomial expansion......which is : (x + c)2 = x2 + c2 + 2xc ......(1) Now, replace x with (a + b) in (1).....then it becomes....... (a + b)2 + c2 + 2.(a + b).c .....(2) Just a little more to be done here ( now we expand (2) in the last step)........ a2 + b2 + 2ab + c2 + 2ac + 2bc (rearranging this we get) a2 + b2 + c2 + 2ab + 2bc + 2ac . this happens to be the expansion for (a + b = c)2
How do you calculate the hypotenuse of a right triangle?
The old pythagorean theorem says, "the square of the hypotenuse is equal to the sum of the square of the other two sides." What that means is, get an accurate measurement of the two sides that touch the right angle, square them and add them together then take the square root of that number and you'll have the length of the hypotenuse. In mathematical terms it's: A2+ B2= C2. The hypotenuse of a right angled triangle is the longest side, or the one opposite the right angle. It can be calculated using a variety of methods - Pythagoras theorem : A2 + B2 = C2, where A and B are the sides adjacent to the right angle, and C is the hypotenuse. The square of A plus the square of B is equal to the square of C, so C can be calculated as √(A2 + B2). Trigonometric angle rules : Sin(e) x = o/h, cos(ine) x = a/h, tan(gent) x = o/a, where x is one of the other two angles, o is the side opposite this angle, a is the side adjacent to it, and h is the hypotenuse. Using these angle rules, you can calculate the length of any of the sides given the length of one of the other sides plus an angle. There are others, but they start to become more difficult to explain without other knowledge in triangle geometry! a2+b2=c2 /l / l / l C / l A / l / l / l /____ l B Example: /l / l / l C / l A=4 / l / l / l /___ l B=3 a2+b2=c2 42+32=c2 16+9=c2 25=c2 square root of 25= square root of c2 5=c Answer: /l / l / l C=5 / l A=4 / l / l / l /____ l B=3 Formula: a2+b2=c2 Example: A=4 B=3 C=? a2+b2=c2 42+32=c2 16+9=c2 25=c2 square root of 25= square root of c2 5=c Answer: A=4 B=3 C=5
Marks will announced or not for CBSE 10th results?
No. This time 2010 only grades will be given for class X. The grades are A1, A2, B1, B2, C1, C2, D, E1 and E2
