Suppose a triangle has two sides of length 3and 4 and that the angle between these two sides is 60. What is the length of the third side of the triangle?

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  A.  √13

Step-by-step explanation:

You can make an educated guess and come to the right conclusion.

The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.

So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:

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A -- between 3 and 4, the correct choice

B -- 3, too short

C -- 1.73, too short

D -- more than 4, too long

__

The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.

  c = √(a^2 +b^2 -2ab·cos(C))

  c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)

  c = √13 . . . . . length of the side opposite the 60° angle

step-by-step explanation:

cats

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form