A ladder leans against a building so that the angle between the ground and the ladder is 30 degrees. If the base of the ladder is 12 feet from the base of the building, what is the length of the ladder? Enter your answer fully rationalized and simplified. Do not enter the decimal answer!!!

Question

directrix · Answer

The ladder length is  twice (12 divided by the square root of 3) = 8 times square root of 3

paxpolaris · Answer

|dw:1330495194219:dw|

anonymous · Answer

I got $$\sqrt{x ^{2}+144}$$
is that right?

paxpolaris · Answer

use the properties of special right triangles ... in this case 30-60-90

directrix · Answer

In a 30-60-90 triangle, the side opposite the 30 angle = 1/2 the hypotenuse of that triangle. The ladder is the 30-leg in this problem. The 12 feet from the ladder foot to the base of the building is the 60-leg. So, the ladder base to building base is 12. To get the 30-leg divide 12 by   √3,then double to get the ladder length which in this problem is the hypotenuse.

2 [ 12 / √3 ] = 8 * √3

anonymous · Answer

thank you!!