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

a. what is the length of the side of the lot opposite the 60° angle b. what is the length of the hypotenuse of the triangular lot.

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

1 answer

Make an effort to memorize the ratio of sides of both the 30-60-90 and the 45-45-90 right-angled triangles, those values will come up again and again in your study of trig.

angles: 30-60-90
sides : 1 - √3 - 2

angles : 45-45-90
sides : 1 - 1 - √2

a)
so set up a ratio:
1/41 = √3/x
x = 41√3 = appr 71.0141

b)
Here is the advantage of knowing the sides of the 30-60-90 triangle
Look at your sketch:
sin30° = 1/2
cos30° = √3/2
tan30° = 1/√3

notice if you know the memorize the ratio of sides in that triangle, and if you know the definitions of the trig rations, you will always have them ready.