1. Each of these cans holds 200 cm. Find the heights of these two cans, What are the heights of the 2 cm - radius can and the 5 cm - radius can respectively?
A
8 cm and 19 cm
B
13.79 cm and 2.45 cm
С
4.0 cm and 25.0 cm
D
15.9 cm and 2.5 cm

If in rectangular coordinates we have a point (x, y), then the angle defined between the x-axis and a ray that connects the point with the origin is defined by:

Tan(θ) = y/x

Cos(θ) = x/(√(x^2 + y^2))

Sin(θ) = y/(√(x^2 + y^2))

Ctg(θ) = x/y

Sec(θ) = √(x^2 + y^2)/x

Csc(θ) = √(x^2 + y^2)/y

Ok, now we have all the equations.

We know that:

Sec(C) = 30/24

Then:

√(x^2 + y^2) = 30

x = 24

Replacing x in the first equation we get:

√(24^2 + y^2) = 30

y = √(30^2 - 24^2) = 18

Then we have:

x = 24

y = 18

√(x^2 + y^2) = 30

So we can just replace these in the equations:

Tan(C) = y/x = 18/24

Cos(C) = x/(√(x^2 + y^2)) = 24/30

Sin(C) = y/(√(x^2 + y^2)) = 18/30

Ctg(θ) = x/y = 24/18

Sec(θ) = √(x^2 + y^2)/x = 30/24

Csc(θ) = √(x^2 + y^2)/y = 30/18