Two boats are traveling toward a cliff that is 150 feet above sea level. When the two boats are exactly 200 feet apart, the boat closest to the cliff has an angle of elevation to the top of the cliff of 22 degree, as shown.

9514 1404 393

  14.71°

Step-by-step explanation:

The tangent relation can be helpful here.

  Tan = Opposite/Adjacent

With reference to the attached diagram ...

  tan(22°) = CD/DA = (150 ft)/DA

  tan(x) = CD/DB = (150 ft)/(DA +200 ft)

Substituting for DA, we find ...

  tan(x) = (150 ft)/((150 ft)/tan(22°) + 200 ft) ≈ 150/(371.26 +200) ≈ 0.262576

  x = arctan(0.262576)

  x ≈ 14.71°

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: