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

A 30°-60°-90° triangle respectively follows the side lengths x-x√(2)-2x.

If the side opposite to the 30° angle is 41, that means x = 41.

The side opposite to the 60° angle is represented by x√(2). Therefore, you have the equation s = x√(2) when s represents the side length. Plugging in x = 41, you get that s = 41√(2), or s = 57.9828.

1. Length of Side = 41√(2) feet. or Length of Side = 57.9828 feet.

The hypotenuse is the side opposite from the 90° angle. The side length is represented by 2x. Therefore the side length, plugging in x = 41, is 2(41) or 82.

2. Length of Hypotenuse = 82 feet.

Finally, the trigonometric calculations for the sine, cosine, and tangent values of 30° can be found using a unit circle, but I'm lazy and am just going to plug it into a calculator for you.

3. sin(30°) = 0.5
cos(30°) = √(3)/2 = 0.866
tan(30°) = sin(30°)/cos(30°) = 0.5/0.866 = 0.5774

Answer 2

Oh, sorry. Decimals rounded to four decimal places. sin(30°) would then equal 0.5000 and cos(30°) would then equal 0.8660.