The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. the top of the ladder is placed an unknown distance off the ground, leaning on the pipe. the ladder and the ground meet at a 56.4° angle. at what angle does the pipe meet the ground?
a.35.7°
b.46.7°
c.55.7°
d.88.2°

This is the concept of applications of geometry trigonometry;
We are required to find the angle at which the pipe meet the ground.
this will be given by sine rule but first we need the distance at which the ladder meet the wall from the ground;
using cosine rule;
c^2=a^2+b^2-2abcos C
c^2=12^2+7^2-2*7*12cos 56.4
c^2=193-92.97
c^2=100.07
thus;
c=10.0015 ft
therefore the angle that is required will be given by:
a/sin A=b/sin B=c/sin C
thus substituting the values we shall have:
10/sin 56.4=12/sin x
12.00775=12/sinx
getting the reciprocal of both sides we get;
0.0833=sinx/12
sinx=0.99935
x=sin-1 0.99935
x=87.94
this is approximately equal to the last option which is d 

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