Question

Help me please !!!! I need to make sure I am correct with my thinking

Answer 1

1.  Use the Pythagoras theorem
13^2 = x^2 + 5^2
solve for x and youll get the height of the roof.

2.  let x = length of the rpoe)-

x^2 = 9^2 + 12^2

3. Pythagoras again 
20^2 = x^2 + 12^2

Answer 2

Problem One
Givens
The length of the ladder is 13 feet.
The distance from the foundation to a point where the ladder is safe to start from = 5 feet.

Find
The height of the house

Formula
a^2 + b^2 = c^2
a =5
b = house height
c = 13

Sub and solve
5^2 + b^2 = 13^2
25 + b^2 = 169       subtract 25 from both sides.
b^2 = 169 - 25
b^2 = 144                Take the square root of both sides.
b =sqrt(144)
b = 12

The house is 12 feet high. <<<<< answer

Problem Two
Givens
height of flagpole = 9
Distance to the hook = 12 feet
Rope length = ??

Formula
a^2 + b^2 = c^2

Sub and solve
9^2 + 12^2 = c^2
81 + 144 = c^2
c^2 = 225 Take the square root of both sides.
sqrt(c^2) = sqrt(225)
c= 15

Problem Three
Givens
T = 1 hour (not needed)
c = 20 miles
b = eastbound boat = 12 miles
a = northbound boat = ????

Formula
a^2 + b^2 = c^2

Sub and solve
a^2 + 12^2 = 20^2
a^2 + 144 = 400       Subtract 144 from both sides.
a^2 = 400 - 144
a^2 = 256                 Take the square root of both sides.
sqrt(a^2) = sqrt(256)
a = 16                      
The northbound  boat has gone 16 miles