Answer:
1). The distance of the foot of the ladder to the nearest foot is 17 (17.3 rounded)
2). The angle the ladder makes with the house to the nearest degree is 12 (12.8 rounded)
Explanation:
1). Use the 30, 60, 90 special right triangles formula (the side opposite of the 30 degree angle is equal to x, the side opposite of the 90 degree angle is equal to 2x, and the side opposite of the 60 degree angle is equal to x square root 3) and you need to find x square root 3. Since you already have 2x (20) you just need to divide that by 2 and you have x. Then, you need to take that number and multiply it by the square root of 3, giving you the answer given to you above.
2). Using trig to find the missing angle, you use cosine (adjacent over hypotenuse) so the equation would equal: cosine(x)=adjacent (19.5) over hypotenuse (20). To get x by itself, you take away cosine from one side and turn it into cosine-1 on the other side of the equation, leaving x by itself. Then you put into your calculator cosine-1 (19.5 over 20), giving you the answer given above .
Hope this helps (: