How do I find the median for a congruent triangle

1 answer:

3 0

The length of a median is equal to half the square root of the difference of twice the sum of the squares of the two sides of the triangle that include the vertex the mediam is drawn from and the square of the side of the triangle the median is drawn to.

triangle sides by a, b, c.

ma=122c2+2b2−a2

mb=122c2+2a2−b2

mc=122a2+2b2−c2

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Use the distributive property to multiply the following binomials

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(x+5)(x-5)
= x^2 - 5x + 5x - 25
= x^2 - 25

(5x+3)(5x-3)
= 25x^2 - 15x + 15x - 9
= 25x^2 - 9

do you see the pattern? both the coefficient on x and constant multiply together to make a perfect square and the middle term, also known as "b" term cancels out leaving a binomial

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3 years ago

Evaluate fog and gof if f(x)=5x-8 and g(x)= x^3

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Answer:

see explanation

Step-by-step explanation:

note that f ○ g = f(g(x))

To evaluate substitute x = x³ into f(x)

f(g(x)) = f(x³) = 5x³ - 8

In the same way

g ○ f = g(f(x))

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3 years ago

Trigonometric Ratios:<br> "First steps in trigonometry"

anygoal [31]

9514 1404 393

Answer:

sin: 0, (√(2-√3))/2, 1/2, (√2)/2, (√3)/2, (√(2+√3))/2, 1

cos are the same values in reverse order

Step-by-step explanation:

Given the side ratios of the "special" right triangles, we know that ...

sin(30°) = cos(60°) = 1/2

sin(45°) = cos(45°) = 1/√2 = (√2)/2

sin(60°) = cos(30°) = (√3)/2

Using the half-angle formulas in the second attachment, we can find exact values for the 15° and 75° angles.

sin(15°) = sin(30°/2) = √((1 -cos(30°)/2) = √((1 -(√3)/2)/2) = (√(2 -√3))/2

cos(15°) = √((1 +cos(30°)/2) = √((1 +(√3)/2)/2) = (√(2 +√3))/2

Then the exact table values are ...

sin(0°) = cos(90°) = 0
sin(15°) = cos(75°) = (√(2-√3))/2
sin(30°) = cos(60°) = 1/2
sin(45°) = cos(45°) = (√2)/2
sin(60°) = cos(30°) = (√3)/2
sin(75°) = cos(15°) = (√(2+√3))/2
sin(90°) = cos(0°) = 1

_____

<em>Additional comments</em>

The numerical sine and cosine values in the attachment are computed by the spreadsheet functions SIN( ) and COS( ). Those functions require an argument in radians. The RADIANS( ) function converts from degrees to radians.

The "special" right triangles are the isosceles right triangle with side ratios 1:1:√2, and the 30°-60°-90° triangle with side ratios 1:√3:2.