<u>Statement Reason </u>
AB║CD , AD║CB Given
m∠BAC = m∠ACD Alternate Interior Angles
m∠ACB = m∠CAD Alternate Interior Angles
AC = AC Reflexive Property of Equality
ΔABC ≅ΔCDA ASA ≅
Answer:
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
-22 = -2x + 9
-31 = -2x
-31/-2 = x
x = 15.5
Using systems of equations, you can find the number of tickets by elimination.
S are students and A are adults.
S+A=8
7.25A+5.50S=52.75
Multiply the first equation by -5.50 to eliminate S.
-5.50A-5.50S=-44
7.25A+5.50S=52.75
1.75A=8.75
8.75÷1.75=5
There were 5 adult tickets and 3 students.