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

The lneth of the side opposite the 30-degree angle in a 30-60-90 triangle is 1/2 the hypotenuse.

So if the side opposite the 30-degree angle has length 41 feet, then the hypotenuse must be 82 feet. Thats part (b)

For part(a), The side opposite the 60-degree angle is 0ne-half the hpotenuse multiplied by the sqrt(3) So the side opposite the 60-degree angle is (1/2)(82) (sqrt(3) = 41 sqrt(3).

Now, e know the measurement of all 3 sides, so, for part (c),

sin 30 = 1/2
cos 30 = sqrt(3)/2
tan 30) = sqrt(3)/3

Answer 2

Read my entire reply, and you will see which is (a), (b), and (c).

Answer 3

ok thanks