A10-foot ladder placed on level ground leans against the side of a house. the ladder reaches a point that is 9.2 feet up on the side of the house. (a) what is the measure of the angle formed by the ladder and the level ground? round your answer to the nearest degree. show your work.

theta = arcsin 0.92 = 1.17 radian, or 66.93 degrees

Step-by-step explanation:

Think of this ladder as the hypotenuse of a right triangle.  The angle formed by the ladder and level ground could be called theta.  Then the side of the triangle "opposite" theta is 9.2 ft, the hypotenuse is 10 ft, and the "adjacent side is unknown.

Our job is to determine the measure of this angle, theta.

Which trig function involves the opp side and the hyp, but not the adj side (whose value we don't know)?  That'd be the sine:

sin theta = opp / hyp = 9.2 ft   /   10 ft = 0.92.

Our last step is to use the inverse sine function to determine the measure of the angle, theta:

theta = arcsin 0.92 = 1.17 radian, or 66.93 degrees.