A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot.

The height of tree house is 70.71 feet

Step-by-step explanation:

We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground

Refer the attached figure

Length of rope AC = Hypotenuse =100 feet

The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =

We are supposed to find the height of tree house i.e.AB = Perpendicular

So, Using trigonometric ratio

Hence The height of tree house is 70.71 feet

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:

x> 6

step-by-step explanation:

8x+8> 7x+14

8x-7x> 14-8

x> 6