A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.

a. Find the length of the side of the lot opposite the 60° angle.

b. Find the length of the hypotenuse of the triangular lot.

c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

Question

A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet.
 
a. Find the length of the side of the lot opposite the 60° angle.
 
b. Find the length of the hypotenuse of the triangular lot.
 
c. Find the sine, cosine, and tangent of the 30° angle in the lot. Write your answers as decimals rounded to four decimal places.

anonymous · Answer

all 30-60-90 triangles are similar... so you can use proportions here.  
also 30-60-90 triangles are special triangles in that their sides have special relationships:

side opposite 30 degrees is HALF of the hypotenuse;
side opposite 60 degrees is (shortest side)*sqrt3

you can use these measurements to find the sin,cos, tan of all the angles in the triangle.