Question

A building 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)

Answer 1

check the picture below.

Answer 2

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