A skateboarder wants to build a ramp to get over a cement wall. The height of the wall is 10 feet. If the ramp is 20 feet long, what is the angle of elevation between the ground and the ramp?

θ = 30°

Angle of elevation is 30°

Step-by-step explanation:

Given;

Height of wall w = 10 ft

Length of ramp l = 20 ft

Angle of elevation = θ

Applying trigonometry;

Sinθ = opposite/hypothenuse

Where;

Height of wall w = opposite (it's opposite the angle of elevation)

Length of ramp l = hypothenuse

Sinθ = w/l

θ = arcsine (w/l)

Substituting the values;

θ = arcsine (10/20)

θ = arcsine (0.5)

θ = 30°

Angle of elevation is 30°

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1