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.

Answer 1

1 : 2 : .

Answer 2

1 2 3

Answer 3

s3 is the sqaure root of three

Answer 4

Ok, so if you look at the figure above. ALL 30-60-90 degree triangles will have this relationship between their sides. (this can be proven via a equilateral triangle but that's not important right now) The point is that the ratio of the various sides are always consistent if the angles are 30-60-90 degree .

Answer 5

So the ratio S2/S3 is always
\[\sqrt{3}\]
the ratio S2/S1 is always
\[\frac{\sqrt{3}}{2}\]
and the ratio s3/s1 is always
\[\frac{1}{2}\]