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.
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.
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