20 me ! will pass out brainliest answer!

1) a 15-foot pole is leaning against a tree. the bottom of the pole is 8 feet away from the bottom of the tree.

approximately how high up the tree does the top of the pole reach?

a. 7.0 feet

b. 12.7 feet

c. 7.0 feet

d. 1.9 feet

2) a tree is 132 inches tall. the distance from the top of the tree to the tip of the tree's shadow is 166 inches.

approximately how long is the tree's shadow?

a. 212 inches

b. 149 inches

c. 101 inches

d. 34 inches

Hello! Lets do this step by step my sweet kitty! ;)
So for the first question to solve we are going to be using the Pythagorean theorem which is  a^2 + b^2 = c^2. So with the given numbers we are going to plug them into our equation. :) So C is the hypotenuse and a and b are gonna be the legs. We don't know what our height is so for that we are going to use the variable of n.  So we get 15^2 = 8^2 + n^2  
So we can rewrite our equation 225 = 64 + n^2  Now to isolate n we are going to subtract 64 from both sides of the equation giving us 161=n^2
Now we find the square root of 161 which is equal to = 12.6885 which can be rounded off to 12.7 which makes B our answer! :)

Problem 2).
We are going to use the same process so plugging in our numbers to the equation just as we did previously gives us 166^2 = 132^2 + n^2
Rewriting the equation as 27556= 17424 +n^2  Now subtract 17424 from both sides leaves us with 10132=n^2 Now just find the square root of 10132 which is 100.657 which can be rounded to about 101 which gives us our answer! Option C 101 inches. :)

Hope I helped! If you have any other questions or would like further explanation just let me know! :) 

Pythagorean theorem
if yo have a right traignel, then
if a and b are legs (sides that touch the right angle) and c is the hypotonuse (longest side and side ooposite right angle)
a^2+b^2=c^2 so

1. 15 foot pole leans agains tree
bottom is 8 feet
we can see a right traignel
the pole is the hypotonuse and 8 is 1 leg so the other leg is the height that the pole reaches
8^2+b^2=15^2
64+b^2=225
subtract 64
b^2=161 take square root of both sides using calculator
b=12.68 ft
closest answer is 12.7
answer is B, 12.7

2. tree is132 tall
distance from tree to shadow is 166
how long is shadow?
tree height is standing height or one of the legs
distance from tree to shadow is 166 aka hypotonuse
shadow=bottom leg so
132^2+b^2=166^2
17424+b^2=27556
subtract 17424 from both sides
b^2=10132 take square root using calculator
b=100.65
closest is 100.1
answer is C, 100.1
diagram below