2b) A farmer is building a pen inside a barn. The pen will be in the shape of a right triangle. The farmer has 14 feet of barn wall to use for one side of the pen and wants another side of
the pen to be 15 feet long.

A)To the nearest tenth of a foot, find all possible lengths for the third side of the triangle.
Show your work.

B)The farmer wants the area of the pen to be as large as possible. What length should he
choose for the third side? Justify your answer.

C)Find the measure of the acute angles for the triangle you described in part b. Round to the
nearest whole degree. Show how you used trigonometric ratios to find the angles.

Step-by-step explanation:

A)

the sum of any two sides of a right triangle more than any other side

14+15>29, x is less than 29

14+x>15

x>1

15+x>14

x>-1

1<x<29

lets use Pythagorean Theorem

14^(2)+15^(2)=c^2

196+225=c^2

421=c^2

plusminus sqrt(421)=c

distance can't be negative, so:

c=sqrt(421)

c=20.5182845287

sqrt(421) is the largest possible right triangle side

1<xsqrt(421)

B) as we can see from above, the largest possible length of the third side is 14/sqrt(421) or about 20.5182845287ft

C)sqrt(421) by 14 by 15

tan(x1)=15/14

x1=tan^-1(15/14)

x1=47 degrees

tan(x2)=14/15

x2=tan^-1(14/15)

x2=43 degrees

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.