Question

A BUILDING IN A CITY LOT IS SHAPED AS A 30 DEGREE -60 DEGREE -90 DEGREE TRIANGLE . THE SIDE OPPOSITE THE 30 DEGREE ANGLE MEASURES 41 FEET. a. FIND THE LENGTH OF THE SIDE OF THE LOT OPPOSITE THE 60 DEGREE ANGLE. b. FIND THE LENGTH OF THE HYPOTENUSE OF THE TRIANGULAR LOT.
c. FIND THE SINE, COSINE, AND THE TANGENT OF THE 30 DEGREE ANGLE IN THE LOT. WRITE YOUR ANSWERS AS DECIMALS ROUNDED TO FOUR DECIMAL PLACES.

Answer 1

@FoolForMath plz help @sally1979

Answer 2

We can do this using trig, or if you haven't done trig functions yet, then something more basic?

Answer 3

The thing about 30-60-90 triangles is, whatever the length of the side opposite the 30 degrees, the length of the side opposite the 90 degree angle (the hypotenuse) will always be double that, and the length of the side opposite the 60 degree angle will always be the length of the side opposite the 30 degree angle, times the square root of 3.
Keeping those in mind,
The length of the side opposite the 60 degree angle is
41 times the square root of 3, just round that off.

The length of the side opposite the 90 degree angle, which is the hypotenuse is
41 times 2, which is 82

The sine of the 30 degree angle in this case is the length of the side OPPOSITE it, divided by the length of the hypotenuse (in this case, 41/82 = 1/2 = 0.5)

The cosine of the 30 degree angle in this case is the length of the side ADJACENT to it, divided by the length of the hypotenuse (try to work this out for yourself, all you need are those above^)

The tangent of the 30 degree angle in this case is the length of the side OPPOSITE it, divided by the length of the side ADJACENT to it, (again, try it for yourself :) )

In time, you'll find that the sines, cosines, etc of angles remain the same, regardless of the size of the triangle.

If I made a mistake, or wasn't clear enough, please let me know :)