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

16-09-2017
Mathematics

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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

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goat4kc goat4kc · Answer 1 · 2017-09-16T03:36:41+02:00

a) Using the special right triangle ratio for 30-60-90 triangles (which is 1-√3-2, opposite sides of the angles respectively, we can find that the side opposite the sixty degree angle is 41√3.

b) The hypotenuse is the same. Using the ratios, we see that the hypotenuse is 82.

c)sin(30)= opp/hyp = 41/82 = 1/2
cos(30)= adj/hyp = 41√3/82 = √3/2
tan(30)= opp/adj = 41/41√3 = 1/√3 = √3/3