A ramp leading into a building makes a 15° angle with the ground. The end of the ramp is 10 feet from the base of the building. Approximately how long is the ramp? Round to the nearest tenth. 10.3 feet 10.4 feet 13.2 feet 38.6 feet

10.4feet

Step-by-step explanation:

The set up wil form a right triangle

Length of the ramp is the hypotenuse

The length of the end of the ramp from the base= 10 feet (adjacent)

Angle of elevation = 15 degrees

Required

Length of the ramp

Using SOH CAH TOA

Cos  theta = adj/hyp

cos 15 = 10/L

L = 10/cos15

L = 10/0.9659

L = 10.35

L ≈ 10.4 feet

Hence the length of the ramp is 10.4feet

step-by-step explanation:

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!