Ill Solve the ff. problems using trigonometric or inverse trigonometric functions
Show illustration, define variables used and give a detailed solutions.
1. In the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the angle a = angle BAD which minimizes the distance L, where L = AD + ED
2. At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest angle.
3. Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9 inches.
4. A statue 10 feet high is standing on a base 13 feet high. If an observers eye is 5 feet above the ground, how far should he stand from the base in order that the angle between his lines of sight to the top and bottom of the statue is a maximum. (How far should he stand to get the best view of the statue.
5. A steel girder 27 feet long is to be moved on rollers along a passageway 8 feet in width and into a corridor at right angles to the passageway. If the horizontal width of the girder is neglected, how wide must the corridor be in order that the girder can go around the corner?