A truck parked on the street is 56 m from the base of the apartment building on the right. The angle of elevation from the truck to the top of the building is 40°. The parked truck is 49 m from the base of the apartment building on the left. The angle of elevation from the truck to the top of that building is 50°. Which building is taller?

The taller building is the second building which is the apartment building on the left with an height of 58.4m

Step-by-step explanation:

This is a Trigonometric question. We solve this using the Tangent formula

tan θ = Opposite side/Adjacent side

We are given 2 buildings

Building 1

tan θ = Opposite side/Adjacent side

θ = Angle of Elevation = 40°

Distance from the base of the building = Adjacent = 56m

Height of the building = Opposite side = unknown

tan 40 = 0pposite/56m

Opposite = tan 40 × 56m

Opposite = 46.989579346m

Approximately = 47m

Height of Building 1 = 47m

Building 2

tan θ = Opposite side/Adjacent side

θ = Angle of Elevation = 50°

Distance from the base of the building = Adjacent = 49m

Height of the building = Opposite side = unknown

tan 50 = 0pposite/49m

Opposite = tan 50 × 49m

Opposite = 58.395926037m

Approximately = 58.4m

Height of Building 2 = 58.4m

The taller building is the second building which is the apartment building on the left with an height of 58.4m

answer: 590

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!