Check the picture below.
make sure your calculator is in Degree mode.
The Lagrangian is

with critical points where the partial derivatives vanish.



Substitute
into the last equation and solve for
:

Then we get two critical points,

We get an absolute maximum of
at the second point, and an absolute minimum of
at the first point.
Sin 30 = 1/2
tan 45 = 1
Cosec 60 = 2 / √3 = 2√3 / 3
cot 45 = 1
Cos 60 = 1/2
sec 30 = 2 / √3 = 2√3 / 3
_______________________________
[ 1/2 + 1 - 2√3/3 ] ÷ [ 1 + 1/2 - 2√3/3 ] = <em>1</em>
The face and denominator of the fraction are exactly the same thus the answer is 1 .
The given question describes a right triangle with with one of the angles as 20 degrees and the side adjacent to the angle 20 degrees is of length 5,000 feet. We are looking for the length of the side opposite the angle 20 degrees.
Let the required length be x, then

Therefore, the height of the airplane above the tower is 1,819.85 feet.
Step-by-step explanation:
First, you have to find what's the height of the shape and you also have to find the base. Then you multiply those together. If there 2 sides, multiply 2 and you will golet your answer.