Abuilding lot in a city is shaped as a 30°-60°-90° triangle, like the figure shown.

the side opposite the 30° angle measures 41 feet.

a) find the length of the side of the lot opposite the 60° angle.(show how i know).

b) find the length of the hypotenuse of the triangular lot.(show how i know)

A) You can find the length of the side of the lot opposite the 60° angle  (which we will call "x") as below:

 Tan(α)=Opposite/Adjacent

 α=60°
 Opposite=41 feet
 Adjacent=x

 When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:

 Tan(60°)=x/41
 (41)Tan(60°)=x
 x=41√3
 x=71.01 feet

 B) Now, you can find the length of the hypotenuse:

 Cos(α)=Adjacent/Hypotenuse

 α=60°
 Adjacent=41 feet
 Hypotenuse=y

 When you substitute these values into Cos(α)=Adjacent/Hypotenuse, you obtain:

 Cos(60°)=41/y
 yCos(60°)=41
 y=41/Cos(60°)
 y=82 feet

Check the picture below.

the answer for the expression is 384