The length and width of a rectangle are consecutive even integers. the area of the rectangle is 80 square units. what are the length and width of the rectangle?

X(x + 2) = 120sq units 

Set it equal to 0 
x^2 + 2x - 120 = 0 

factor 
(x + 12)(x - 10) 

For the shorter side: 
x - 10 = 0 
x = 10 

Now that you have x, solve for the longer side which we said was represented by 
x + 2 
10 + 2 = 12 

Proof 
A = L x W 
120 = 10 x 12 
120 = 120 
true 

Our length is 12 and our width is 10

The formula used will be:

tan 42° = y/115

Step-by-step explanation:

Lets simplify the the question.

We have a boat which is situated at 115 meters away from a light house. It forms the base of the right angled triangle.

We need to find the distance from the bottom of the light house to the top of the light house. This distance is the height of the lighthouse, which forms the perpendicular side of the right angled triangle.

The distance between boat and top of the lighthouse is unknown, it forms the hypotenuse.

The angle of elevation, which is the angle between base and hypotenuse, is given as 42°.

The right angled formed is shown below.

We know that

tanθ = Perpendicular / Base

tan42 = height / 115

If height= y

tan 42° = y/115

Solve for y.

y = 103.55 meters