(draw a diagram modeling the scenario and solve. round all decimals to the nearest tenth. ) a 15-foot ladder is leaning against a tree. if the ladder reaches 10 feet high on the tree, how far is the base of the
ladder from the tree?

11.18 feet

Step-by-step explanation:

This is a pythagorean theorem problem.  You should draw a ladder as a diagonal line with the top resting on a vertical line (the wall) an the bottom on a horizontal line (the ground.  Then the ground and the wall should connect to make a right tiangle.  

The ladder is the c in a^2+b^2=c^2, and the wall and ground can be either.  I am going to call the wall b which will make the ground a.  So now we have

a^2 + b^2 = c^2

a^2 + 10^2 = 15^2

a^2 + 100 = 225

a^2 = 125

a = 11.18

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9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841